Use and Evaluate Square Roots and Cube Roots: CCSS.Math.Content.8.EE.A.2 - 8th Grade Math

A square root asks "which number, when multiplied by itself, produces this number?" When you're calculating the square root of a decimal, then, it is important to remember what happens when decimals are multiplied When you multiply decimals, you need to count up the decimal places in the input values and that becomes the number of decimal places in the product. Since has two decimal places, that means that the number to be multiplied by itself should have one. , so the answer is .

A square root asks you "what number, when squared, gives you this number?" Here they're asking which number, squared, would give you . Since , that means that the correct answer is .

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is and between the third and fourth terms, the GCF is 4. Thus, we obtain . Setting each factor equal to zero, and solving for , we obtain from the first factor and from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept .

Here the problem is asking you which number, when multiplied by itself, produces . In other words, it's asking you for the square root of , or "what is ?"

When is multiplied by , the result is . Meaning that , so .

Note here that the problem asks which of the following COULD be . Technically is also equal to so could also be , and that is why the problem makes that point clear.

When you're asked to take the square root of a number, the question is asking "which number, when squared, gives you this number?" Here they're asking, then, which number times itself will produce . The answer, then, is , since .

With roots, you can also use the rule that the square root of an entire fraction is equal to the square root of the numerator divided by the square root of the denominator. Here that means that is equal to . And the square roots of 1 and 4 are each integers, so that allows you to calculate to the answer .

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically.

In order to solve this problem using algebra, we need to isolate the on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically.

In order to solve this problem using algebra, we need to isolate the on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically.

In order to solve this problem using algebra, we need to isolate the on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically.

In order to solve this problem using algebra, we need to isolate the on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cube root:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically.

In order to solve this problem using algebra, we need to isolate the on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cubed root:

We can solve this problem one of two ways: first we can ask ourselves the question:

"What number cubed is equal to "

If you aren't sure of the answer to this question, then you can solve the problem algebraically.

In order to solve this problem using algebra, we need to isolate the on one side of the equation. Remember that operations done to one side of the equation must be performed on the opposite side.

We will solve this equation by performing the opposite operation of cubing a number, which is taking the cube root:

A square root asks "what number, when squared, gives you this number?" So is asking for which number, when multiplied by itself, is equal to 144. That number is , since . Note that when the "radical sign" - the bracket surrounding 144 here - is used, mathematically that means that the question is asking for the "principal square root," which means the positive (or "nonnegative") square root. Technically also equals , too, but the radical sign tells you that they just want the positive answer, 12.

Here you should see that, were there no decimals, you’d be looking at . But of course there are decimals so it’s not quite that straightforward. When you multiply decimals, you need to count up the decimal places in the input values and that becomes the number of decimal places in the product. Since has two decimal places, that means that the number to be multiplied by itself should have one. , so the answer is .

A square root asks you "what number, when squared, gives you this number?" Here they're asking which number, squared, would give you . Since , that means that the correct answer is .

A square root asks you "which number, when multiplied by itself, produces this number?" So this problem wants to know which number, when squared, gives you . Note that even if you don't immediately see that , you can use the answer choices to your advantage. You should memorize that and . And when numbers that end in zero are squared, they always produce numbers that end in zero, too. So and , leaving as the correct answer.

When you're taking the square root of a fraction, one thing you can do is express it as two different square roots: the square root of the numerator over the square root of the denominator. So this problem could also be expressed as:

What is ?

Here you can take two fairly straightforward square roots. and , so your answer is .

A square root asks you "what number, when multiplied by itself, equals this number?" Here you're told that , meaning that when a number is multiplied by itself, the product doesn't change. This should get you thinking about two multiplication rules:

Anything times 1 doesn't change. That means that if you want a number to not change when you multiply it, multiply it by 1. , so fits the description here.

Anything times 0 equals 0. That means that if you start with 0, whatever you multiply it by you still have 0. , so also fits the description here.

Of these, only 1 is an actual answer choice, so 1 is the correct answer.

A square root asks "which number, when multiplied by itself, produces this number?" When you're calculating the square root of a decimal, then, it is important to remember what happens when decimals are multiplied When you multiply decimals, you need to count up the decimal places in the input values and that becomes the number of decimal places in the product. Since has two decimal places, that means that the number to be multiplied by itself should have one. , so the answer is .

A square root asks you "what number, when squared, gives you this number?" Here they're asking which number, squared, would give you . Since , that means that the correct answer is .

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is and between the third and fourth terms, the GCF is 4. Thus, we obtain . Setting each factor equal to zero, and solving for , we obtain from the first factor and from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept .