How to find the square root

Help Questions

SSAT Middle Level Quantitative › How to find the square root

Questions 1 - 10

Evaluate: $\sqrt{100} + \sqrt{49 } - \sqrt{36}$

Explanation

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

$\sqrt{100} = 10$

$\sqrt{49 } = 7$

$\sqrt{36} = 6$

$\sqrt{100} + \sqrt{49 } - \sqrt{36} = 10 + 7 - 6 = 17-6 = 11$

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 $43 \cdot 43 = 1,849$ .

Evaluate:

$\sqrt{\frac{169}{100}}$

$\frac{13}{10}$

$-\frac{13}{10}$

$\frac{10}{13}$

$-\frac{10}{13}$

$\sqrt{\frac{169}{100}}$ is undefined.

Explanation

To find the square root of a fraction, extract the square root of both the numerator and the denominator. Since $10 ^{2} = 10 \times 10 = 100$ , $\sqrt{100} = 10$ , and since $13^{2} = 169$ , $\sqrt{169} = 13$ .

Combine these results:

$\sqrt{\frac{169}{100}} = \frac{\sqrt{169}}{\sqrt{100}} = \frac{13}{10}$

$\textup{Simplify fully: }(\sqrt64)(\sqrt4)$

$\sqrt256$

$\sqrt16$

Explanation

First we must simplify the square roots.

$\sqrt64=8$

Because 8 times 8 = 64

$\sqrt4=2$

Because 2 times 2 = 4

Now we have:

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

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 $18^{2}<x^{2}<19^{2}$ , or, equivalently, $324 <x^{2}<361$

All four choices fall in this range.

Evaluate:

$\sqrt{169}$

Explanation

The square root of a number is the number which, when multiplied by itself, yields that number. Since $13 \cdot 13 = 169$ , $\sqrt{169} = 13$ .

$\textup{Simplify: }\sqrt49+\sqrt16-\sqrt25$

$\sqrt40$

$\sqrt6$

Explanation

We must first simplify all of the square roots.

$\sqrt49=7$

Because 7 times 7 =49

$\sqrt16=4$

Because 4 times 4 =16

$\sqrt25=5$

Because 5 times 5 = 25

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

The answer is 6!

Which of the following statements is true about $\sqrt{441}$ ?

$\sqrt{441} = 21$

$\sqrt{441} = 19$

$19 < \sqrt{441} < 20$

$20 < \sqrt{441} < 21$

$21 < \sqrt{441} < 22$

Explanation

The square root of a number is the number which, when multiplied by itself, yields that number. Since $21 \cdot 21 = 441$ , $\sqrt{441} = 21$ .

Which of the following statements is true about $\sqrt{ 231}$ ?

$15 <\sqrt{ 231} < 16$

$16 <\sqrt{ 231} < 17$

$17 <\sqrt{ 231} < 18$

$\sqrt{ 231} = 19$

$\sqrt{ 231} = 17$

Explanation

The square root of a number is the number which, when multiplied by itself, yields that number. Since $15 \cdot 15 = 225$ , $16 \cdot 16 = 256$ , and

$15^{2} = 225 < 231 < 256 = 16^{2}$

then

$15 = \sqrt{225 }< 231 <\sqrt{ 256} = 16$

Evaluate:

$\sqrt{0.0009}$

$\sqrt{0.0009}$ is an undefined quantity.

Explanation

$0.0009= \frac{9}{10,000}$ , so

$\sqrt{0.0009} = \sqrt{\frac{9}{10,000}}$ .

The square root of a fraction can be determined by taking the square roots of both numerator and denominator. Since $3^{2} = 9$ , $\sqrt{9 } = 3$ , and since $100^{2} = 10,000$ , $\sqrt{10,000} = 100$ . Therefore,