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# Square Root and Cube Root Questions

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41 / 74

Choose the correct option.

If $$\sqrt{3^n}=729$$,then the value of n is,

A6

B8

C10

D12

Explanation:

$$\sqrt{3^n}=729=3^6 \Leftrightarrow p^2=\frac{0.13}{13}=\frac{1}{100} \Leftrightarrow p=\sqrt{\frac{1}{100}}=\frac{1}{100}=\frac{1}{10}$$
$$=0.1$$

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42 / 74

Choose the correct option.

$$28\sqrt{?}+1426=\frac{3}{4}$$ of 2872

A576

B676

C1296

D1444

Explanation:

Let, $$28\sqrt{x}+1426=3\times718$$
Then,$$28\sqrt{x}=2154-1426 \Leftrightarrow 28\sqrt{x}=728$$
$$\sqrt{x}=26 \Leftrightarrow x=(26)^2=676$$

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43 / 74

Choose the correct option.

If $$\sqrt{x}\div\sqrt{441}=0.02$$, then the value of $$x$$ is:

A0.1764

B1.764

C1.64

D2.64

Explanation:

$$\frac{\sqrt{x}}{\sqrt{441}}=0.02 \Leftrightarrow \frac{\sqrt{x}}{21}=0.02 \Leftrightarrow \sqrt{x}=0.02\times21=0.42$$
$$\Leftrightarrow x=(0.42)^2=0.1764$$

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44 / 74

Choose the correct option.

$$\sqrt{\frac{.0196}{?}}=0.2$$

A0.49

B0.7

C4.9

DNone of these

Explanation:

$$\sqrt{\frac{.0196}{x}}=0.2$$
Then,$$\frac{.0196}{x}=0.04 \Leftrightarrow x=\frac{.0196}{.04}=\frac{1.96}{4}=4.9$$$$\sqrt{\frac{.0196}{x}}=0.2$$
Then,$$\frac{.0196}{x}=0.04 \Leftrightarrow x=\frac{.0196}{.04}=\frac{1.96}{4}=4.9$$

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45 / 74

Choose the correct option.

$$\sqrt{0.0169\times?}=1.3$$

A10

B100

C1000

DNone of these

Explanation:

Let $$\sqrt{0.0169\times x}=1.3$$
Then, $$0.0169x=(1.3^2)=1.69 \Leftrightarrow x=\frac{1.69}{0.0169}=100$$

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46 / 74

Choose the correct option.

$$\sqrt{1369}+\sqrt{.0615+x}=37.25$$,then xis equal to:

A$$10^{-1}$$

B$$10^{-2}$$

C$$10^{-3}$$

DNone of these

Explanation:

$$37 + \sqrt{0.0615+x}=3725 \Leftrightarrow \sqrt{.0615+x}=0.25$$
$$\Leftrightarrow .0615+x=(0.25)^2=0.0625 \Leftrightarrow x=.001=\frac{1}{10^3}=10^{-3}$$

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47 / 74

Choose the correct option.

Three-fifth of the square of a certain number is 126.15.what is the number?

A14.5

B75.69

C145

D210.25

Explanation:

Let the number be x. then,
$$\frac{3}{5}x^2=126.15 \Leftrightarrow x^2=\left(126.15\times\frac{5}{3}\right)=210.25$$
$$\Leftrightarrow x=\sqrt{210.25}=14.5$$

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48 / 74

Choose the correct option.

If $$\sqrt{1+\frac{55}{729}}=1+\frac{x}{27}$$,then the value of x is:

A1

B3

C5

D7

Explanation:

$$\sqrt{1+\frac{55}{729}}=1+\frac{x}{27} \Rightarrow \sqrt{\frac{784}{729}}=\frac{27+x}{27} \Rightarrow \frac{27}{28}=\frac{27+x}{27}$$
$$\Rightarrow 27+x=28 \Rightarrow x=1$$

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49 / 74

Choose the correct option.

By how much does $$\sqrt{12}+\sqrt{18}$$ exceed $$\sqrt{3}+\sqrt{2}$$ ?

A$$\sqrt{2}-4\sqrt{3}$$

B$$\sqrt{3}+2\sqrt{2}$$

C$$2(\sqrt{3}-\sqrt{2})$$

D$$3(\sqrt{3}-\sqrt{2})$$

Explanation:

$$(\sqrt{12}+\sqrt{18})-(\sqrt{3}+\sqrt{2})=(\sqrt{4\times3}+\sqrt{9\times2})-(\sqrt{3}+\sqrt{2})$$
=$$(2\sqrt{3}+3\sqrt{2})-(\sqrt{3}+\sqrt{2})=(2\sqrt{3}-\sqrt{3})+(3\sqrt{2}-\sqrt{2})$$
=$$\sqrt{3}+2\sqrt{2}$$

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Choose the correct option.

$$\sqrt{\frac{48.4}{0.289}}$$ is equal to:

A$$1\frac{5}{17}$$

B$$12\frac{16}{17}$$

C$$129\frac{7}{17}$$

D$$12\frac{1}{17}$$

Explanation:

$$\sqrt{\frac{48.4}{0.289}}=\sqrt{\frac{48.400}{0.289}}=\sqrt{\frac{48400}{289}}=\frac{220}{17}=12\frac{16}{17}$$

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