How to find the square root

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SSAT Middle Level Quantitative › How to find the square root

Questions 1 - 10
1

Evaluate:

Explanation

Find the individual square roots and perform the operations on them.

2

The square root of a number is 43. What is that number?

Explanation

By definition, the square root of a number multiplied by itself yields that number. Therefore, 43 is the square root of .

3

Evaluate:

is undefined.

Explanation

To find the square root of a fraction, extract the square root of both the numerator and the denominator. Since , , and since , .

Combine these results:

4

Explanation

First we must simplify the square roots.

Because 8 times 8 = 64

Because 2 times 2 = 4

Now we have:

When two parentheses are beside each other, that means muliply.

5

Which of the following numbers has a square root between 18 and 19?

All of these numbers have square roots between 18 and 19.

Explanation

For the square root of a number to fall between 18 and 19, the number has to fall between the squares of these numbers - that is:

If , then , or, equivalently,

All four choices fall in this range.

6

Evaluate:

Explanation

The square root of a number is the number which, when multiplied by itself, yields that number. Since , .

7

Explanation

We must first simplify all of the square roots.

Because 7 times 7 =49

Because 4 times 4 =16

Because 5 times 5 = 25

Now we plug all of these into the original equation to get:

The answer is 6!

8

Which of the following statements is true about ?

Explanation

The square root of a number is the number which, when multiplied by itself, yields that number. Since , .

9

Which of the following statements is true about ?

Explanation

The square root of a number is the number which, when multiplied by itself, yields that number. Since , , and

then

10

Evaluate:

is an undefined quantity.

Explanation

, so

.

The square root of a fraction can be determined by taking the square roots of both numerator and denominator. Since , , and since , . Therefore,

.

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