Squares / Square Roots - SSAT Middle Level Quantitative

Card 0 of 108

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If , then $x=\pm 7$ .

$\left | 7 \right |=7,\ \left | -7 \right |=7$

Therefore, $\left | x \right |+7=7+7=14$ .

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

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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, $324 $<x^{2}$<361$

All four choices fall in this range.

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

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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?

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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 58. What is that number?

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

$58 \cdot 58 = 3,364$ .

$$\frac{\sqrt{64}$-$\sqrt{36}$}{$\sqrt{4}$}=$

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First, find the square root of each number:

$$\sqrt{64}$=8$

$$\sqrt{36}$=6$

$$\sqrt{4}$=2$

Then, solve the equation accordingly.

$$\frac{8-2}{2}$=$

$$\frac{2}{2}$=1$

The answer is

Evaluate: $\sqrt{121}$

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The square root of a number is the number which, when multiplied by itself, yields that number. Since $11 \cdot 11 = 121$ , $$\sqrt{121}$ = 11$ .

Evaluate:

$\sqrt{169}$

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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$ .

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

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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 $\sqrt{ 231}$ ?

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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

then

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

A square has an area of $16\ $ft^{2}$$ .

How long is each of its sides?

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The two sides of the square must be the same length, and multiply to give 16. So we are looking for the $\sqrt{16}$ which is .

Which of the following statements is true about $\sqrt{-225}$ ?

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A negative number does not have a real square root, so this is the correct choice.

Evaluate:

$\sqrt{121}$ + $\sqrt{49}$

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$11 ^{2 } = 11 \times 11 = 121$ , so $$\sqrt{121}$ = 11$ .

$7 ^{2 } = 7 \times 7 = 49$ , so $$\sqrt{49}$ = 7$ .

$$\sqrt{121}$ + $\sqrt{49}$ = 11 + 7 = 18$

Let $N = $\sqrt{10 \times 20 + 7 \times 8}$$

Which of the following is a true statement?

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$N = $\sqrt{10 \times 20 + 7 \times 8}$= $\sqrt{200 + 56}$= $\sqrt{256}$$

Since , $N = $\sqrt{256}$ = 16$

Let $N = $$\sqrt{7^{2}$$$-5^{2}$$-3^{2}$}$

Then which of the following statements is correct?

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$N = $$\sqrt{7^{2}$$$-5^{2}$$-3^{2}$} = $\sqrt{49-25-9}$ = $\sqrt{24-9}$ = $\sqrt{15}$$

, so

$\sqrt{9}$ < $\sqrt{15}$ < $\sqrt{16}$

Which of the answer choices is equivalent to $2$\sqrt{3}$$ ?

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can also be written as $\sqrt{4}$ , so $2$\sqrt{3}$$ can also be written as $\sqrt{4\cdot 3}$ , or $\sqrt{12}$ .

Which of the answer choices is equivalent to $\sqrt{24}$ ?

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Recognize that $\sqrt{24}$=$\sqrt{4\cdot 6}$ . Since $$\sqrt{4}$=2$ , we can move the outside of the radical sign. This leaves us with $2$\sqrt{6}$$ .

What is the square root of ?

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The square root of is , since $7\cdot7=49$ .

Evaluate:

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

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

Combine these results:

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

Evaluate:

$\sqrt{0.0009}$

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$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 , $$\sqrt{9 }$ = 3$ , and since , $$\sqrt{10,000}$ = 100$ . Therefore,

$$\sqrt{0.0009}$ = $\sqrt{\frac{9}{10,000}$} = $\frac{\sqrt{9}$}{$\sqrt{10,000}$} = $\frac{3}{100}$ = 0.03$ .