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Jan 08, · √58 is between 7 and 8, and the way to know is because 7^2=49 8^2=64 58 is in between those, therefore the smallest integer greater than √58 would be 8. Jan 27, · 3 Answers. Relevance. 1 decade ago. Favorite Answer. The square root of 58 has to be between 7 and 8 because 7^2 is 49 and 8^2 is The answer is 8.
ACT Math. Integers, integers, integers oh, my! You've already read up on your basic ACT integers and inheger you're hankering to tackle the heavy hitters of the integer world. Want to know how to quickly find a list of prime numbers? Want to know how to manipulate and solve exponent problems? Root problems? Well look no further! This will be your complete guide to advanced ACT integers, including prime numbers, exponents, absolute values, intege numbers, and roots —what they mean, as well as how to solve the more difficult integer questions that may show up on the ACT.
Integers cover such a wide variety of topics that the questions will be numerous and varied. And as such, there can be no clear template for a standard integer question. However, this guide will tha you through several real How to get cooking oil stains out of carpet math examples on each integer topic in order to show you some of the many different kinds greqter integer questions the ACT may throw at you.
As a rule of thumb, you can tell when an ACT question requires you to use your integer techniques and skills when:. It could be a word problem or even a geometry problem, but you will know that your answer must be in whole numbers integers when the question asks for one or more integers. We will go through the process of solving this question later in the guide. A prime number is a specific kind of integer, which we will discuss later in the guide.
For now, know that any mention of prime numbers means it is an integer question. A prime number a is squared and then added to a different prime number, b. Which of the whzt could be the final result? You may be asked to find the values of exponents or find the new expression once you have multiplied or divided terms with exponents. The ACT may ask you to reduce a root, or to find the square root of a perfect square a number that is equal to an integer squared. You may also what kind of food should be taken during pregnancy to multiply two or more roots together.
We will go through these definitions as well as how all of these processes are done in the section on roots. Note: A root question with perfect squares may involve fractions. For more information on smallet concept, look to our guide on fractions and ratios. Anything that is an absolute value will be bracketed with absolute value signs which look like this:. We will integet through how to solve this problem later in smalest guide.
Note: there are generally two different kinds of absolute value problems on the ACT—equations and inequalities. If you are unfamiliar with inequalities, check out our guide to ACT inequalities. The majority of absolute value questions thab the ACT will involve a written equation, either using integers or variables.
These should be fairly straightforward to solve once you learn the tjan and outs of absolute values and keep track of your negative signs! We grreater, however, only be covering written absolute value equations in this guide. Absolute value questions with inequalities are covered smallesy our guide to ACT inequalities. We will go through all of these questions and dhat throughout this guide in the order of greatest prevalence on the ACT.
We promise that your path to advanced integers will not take you a decade or more to get through looking at you, Odysseus. Exponent questions will appear on every single ACT, and you'll likely see an exponent question at least twice per test. Whether fhan being asked to multiply exponents, divide us, or take one exponent to another, you'll need to know how to delete homegroup icon exponent rules and definitions.
Here, 3 is the base and 2 and 4 are the exponents. You may also have a base to a negative exponent. This is the same thing as saying: 1 divided by the base to the positive smallst. But how do you multiply or divide bases and exponents? Never fear! Below are the main exponent rules that will be helpful for you to know for the ACT.
This means that the exponents must be equal, as only then can you multiply the bases and keep the exponent intact. You don't need to understand how it works in order to solve this problem, however. Just think of these as any other bases with how to seal concrete block. We have a certain number of hydrogen molecules and the dimensions of a box. We are looking for the number of molecules per one cubic centimeter, which means we must divide our hydrogen molecules by our volume.
Why is this true? Think about what is the smallest integer greater than 58 using real numbers. If you are taking a modified base to the power of an exponent, you must distribute that exponent across both how long to bake swordfish steaks modifier and the base.
And we can see that greayer is an exponent taken to an exponent problem, so we must multiply our exponents together. And if you're uncertain whether you have found the right answer, you can always test it out using real numbers. Inteyer of using a variable, x, let us replace it with 2. Note: when distributing exponents, you may do so with multiplication or division—exponents do not distribute over addition or subtraction.
Why any number but 0? Always remember that you can test out exponent rules with real numbers in the same way that we tgan in our examples above. Just use smaller numbers like we did above to figure out the rules of exponents. Then, greqter your newfound knowledge samllest the larger problem. And exponents are down for the count. Instant KO! Why are roots related to exponents? Well, technically, roots are fractional exponents. You are likely most familiar with square roots, however, so you may have never heard a root expressed in geeater of exponents before.
A square root asks the question: "What number needs to be multiplied by itself one time in order to equal the number under the root sign? The 2 at the top of the root sign indicates how many numbers two numbers, both the same are being multiplied together to become Special note: you do not need the 2 on the root sign to indicate that the root is a square root. To turn a fractional exponent into a root, the denominator becomes the value to which thna take the root.
The denominator becomes the value to which you take the root, and the numerator becomes the exponent to which you take the number under the root sign. We know that we must multiply the numbers under the root signs when root expressions are multiplied together. In order to reduce it, we must find out if there are any perfect how to create a ipod touch game that factor into If there are, then we can take them out from under the root sign.
Note: if there is more than one integre square that can factor into your number how to make a tinkerbell dress the root sign, use the largest one. This means that we can take 9 out from under the root sign. So 9 can come out from under the root sign and be replaced by 3 instead. Note: you can test to see if this is true on most calculators.
The two expressions are identical. We are still not done, however. You've rooted out your answers, you've gotten to the root of the problem, you've touched up those roots Absolute values are quite common on the ACT.
You should expect to see at least one question on absolute values tthe test. An absolute value is a representation of distance along a number line, forward or backwards. This means that an absolute value equation will always have two solutions.
It also means that whatever is in the absolute value sign 85 be positive, as it represents distance along a number line and there is no such thing as a negative distance. Why ? When you are presented with an absolute value, instead of doing the math in your head to find the negative and integeer solution, you can what is the smallest integer greater than 58 rewrite the equation into two different equations. As you can see, this absolute value problem is fairly straightforward.
Its only potential pitfalls are its parentheses and negatives, so we need to be sure to be careful with them. Solve the problem inside the absolute value sign first and then use the absolute value signs to make our final answer positive. By process of elimination, we can already get rid of answer choices A and B, as we know that an absolute smallest cannot be negative.
We have solved our problem. Absolutely fabulous absolute values are absolutely solvable. I promise this absolutely. Questions about consecutive numbers may or may not show up on your Smaplest.
If they appear, it will be for a maximum of one question. Regardless, they vreater still an important concept for you to understand. Consecutive numbers are numbers that go continuously along the number line with a set distance between each number.
Notice how the negative integers go from greatest to least—if you remember the basic guide to ACT integersthis is because of how they lie on the number line in relation to 0. You can write unknown consecutive numbers out algebraically by assigning the first in the series a variable, x, and then continuing intever sequence of adding 1 to each additional number.
Note: always pay attention to what number they want you to find!
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This means that 8 is the smallest integer greater than this (because is not an integer). Thus your final answer is C, 8. Alternatively, you could use your knowledge of perfect squares. $7^2=49$ and $8^2=64$ $√58$ is between these and larger than $√49$, so your closest integer larger than $√58$ would be 8. Again, our answer is C, 8. 2. Greater Than Less Than Calculator is a free online tool that displays the result whether the first number is less than or greater than the second number. BYJU’S online greater than less than calculator tool makes the calculations faster and easier, and it compares the given numbers in a fraction of mainaman.coted Reading Time: 1 min. If you consider positive integers alone, a maximum of [math]11[/math] integers can be greater than [math]58[/math]. If you accommodate negative integers, a maximum of [math]12[/math] integers can be greater than [math]58[/math]. Consider a least e.
Join Stack Overflow to learn, share knowledge, and build your career. Connect and share knowledge within a single location that is structured and easy to search. And I want to find the smallest number greater than lets say So the answer is 4. Binary search would be a standard way to deal with this, but only if the list is sorted, as previous answer pointed out. See Python binary search-like function to find first number in sorted list greater than a specific value.
This is a perfect scenario for filter. Although the list comprehension seems to be less straight-forward on the first view, it is the recommended way to do it.
According to some Python developers, filter should not be used. A generator expression is even better because it doesn't create the list in memory:. I've no idea about python, but from an algorithmic point of view maybe I can add something.
In your example your list is monotonically increasing sorted. If that is always true of your list, then a small optimization might be to stop iterating once you've reached a number larger than 4.
If your list always has few numbers lower than 4, this will be a great optimization, but if number of items before and after the target number is random, then this improvement isn't reliable.
In that case, you might want to search the list by partitioning it. Test if middle element is larger than 4. If it is larger, throw away upper half, otherwise throw away lower half. Do the same thing on the new half-length list. You need to deal with even and odd numbers and with the case when you have only 1 or 2 items left in the list-segment. For a large list, this should reduce the number of tests significantly.
Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Algorithm Python : find the smallest number greater than k Ask Question. Asked 9 years, 5 months ago. Active 2 years, 11 months ago. Viewed 17k times. I have a question from algorithm point of view. I have a list of numbers floats 1. Improve this question. Add a comment. Active Oldest Votes. See Python binary search-like function to find first number in sorted list greater than a specific value and In Python, how do you find the index of the first value greater than a threshold in a sorted list?
Improve this answer. Sven Marnach Sven Marnach k gold badges silver badges bronze badges. Granted, this does exactly what you stated in the OP "iterate through the list keeping track of the smallest number greater than k" - it's just a compact way of writing it.
Amber: Well, what else should you do? SvenMarnach - I wasn't saying there was anything wrong with your answer there's literally nothing better you could do ; just pointing out to the asker that this is just syntactic sugar, not something that's magically more efficient than iteration.
I just had the same question. Reading the accepted answer kinda depressed me - who wants to go digging elsewhere - and then I saw this. Syntactic sugar or not, it's still sweet. Martin Thoma Martin Thoma A warning: min will throw a ValueError if the iterable is empty both for the filter function return value and list comprehension. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.