Square Roots

Square Roots on the ACT Math Test

Square roots are also known as radicals. Algebra questions on the ACT math test will assess your knowledge of square roots.

You will need to know how to perform the operations of multiplication and division on square roots.

You will also see problems that have square roots and exponents.

Our download covers all of the skill areas assessed on the math part of the real test.

Here are some  sample problems from our download.

1) What is the product of 20 and the square root of 144?

A. 2880

B. 1728

C. 1440

D. 280

E. 240

The correct answer is E.

First of all find the square root of 144.

The square root is the number that equals a given result when multiplied by itself.

12 × 12 = 144

So the square root of 144 is 12.

Then multiply to find the product.

20 × 12 = 240

2) Which of the answers below is equal to the following radical expression?square root of 45

A. 1 ÷ 45

B. 5 times square root of 9

C.9 times square root of 5

D. 3 times square root of 5

E. 5 times square root of 3

The correct answer is D.

For elementary algebra problems like this one, you need to remember certain mathematical principles.

First, remember to factor the number inside the square root sign.

The factors of 45 are:

1 × 45 = 45

3 ×15 = 45

5 × 9 = 45

Then look to see if any of these factors have square roots that are whole numbers.

In this case, the only factor whose square root is an whole number is 9.

Now find the square root of 9.

square root of 9

= 3

Finally, you need to put this number at the front of the square root sign and put the other factor inside the square root sign in order to solve the problem.

3 times square root of 45

Go back to the Elementary Algebra Questions.

Have a look at our other Free Preparation Materials.