Squares / Square Roots

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SSAT Middle Level Quantitative › Squares / Square Roots

Questions 1 - 10

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

Explanation

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

$\sqrt{100} = 10$

$\sqrt{49 } = 7$

$\sqrt{36} = 6$

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

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 $43 \cdot 43 = 1,849$ .

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 $43 \cdot 43 = 1,849$ .

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

$\sqrt256$

$\sqrt16$

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.

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.

Evaluate:

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

$\frac{13}{10}$

$-\frac{13}{10}$

$\frac{10}{13}$

$-\frac{10}{13}$

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

Explanation

Combine these results:

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

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.

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.

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