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# Square Root and Cube Root Questions

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51 / 74

Choose the correct option.

The value of $$\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}$$ is:

A$$\frac{3}{4}$$

B$$1\frac{1}{3}$$

C$$1\frac{7}{9}$$

D$$1\frac{3}{4}$$

Explanation:

$$\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}=\frac{\sqrt{16\times5}-\sqrt{16\times7}}{\sqrt{9\times5}-\sqrt{9\times7}}=\frac{4\sqrt{5}-4\sqrt{7}}{3\sqrt{5}-3\sqrt{7}}=\frac{4(\sqrt{5}-\sqrt{7})}{3(\sqrt{5}-\sqrt{7})}=\frac{4}{3}=1\frac{1}{3}$$

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52 / 74

Choose the correct option.

If $$3\sqrt{5}+\sqrt{125}=17.88$$, then what will be the value of $$\sqrt{80}+6\sqrt{5}$$ ?

A13.41

B20.46

C21.66

D22.35

Explanation:

$$3\sqrt{5}+\sqrt{125}=17.88 \Rightarrow 3\sqrt{5}+\sqrt{25\times5}=17.88$$
$$\Rightarrow 3\sqrt{5}+5\sqrt{5}=17.88 \Rightarrow 8\sqrt{5}=17.88 \Rightarrow \sqrt{5}= 2.235$$

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53 / 74

Choose the correct option.

Given $$\sqrt{2}=1.414$$ the value of $$\sqrt{8} + 2\sqrt{32}-3\sqrt{128}+4\sqrt{50}$$ is:

A8.426

B8.484

C8.526

D8.876

Explanation:

Given Exp. $$\sqrt{4\times2}+2\sqrt{16\times2}-3\sqrt{64\times2}+4\sqrt{25\times2}$$
$$=2\sqrt{2}+8\sqrt{2}-24\sqrt{2}+20\sqrt{2}=6\sqrt{2}=6\times1.414=8.484$$

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54 / 74

Choose the correct option.

The approximate value of $$\frac{3\sqrt{12}}{2\sqrt{28}}\div\frac{2\sqrt{21}}{\sqrt{98}}$$ is:

A1.0605

B1.o727

C1.6007

D1.6026

Explanation:

Given exp. $$=\frac{3\sqrt{12}}{2\sqrt{28}}\times\frac{\sqrt{98}}{2\sqrt{21}}=\frac{3\sqrt{4\times3}}{2\sqrt{4\times7}}\times\frac{\sqrt{49\times2}}{2\sqrt{21}}=\frac{6\sqrt{3}}{4\sqrt{7}}\times\frac{7\sqrt{2}}{2\sqrt{21}}$$
$$=\frac{21\sqrt{6}}{4\sqrt{7\times21}}=\frac{21\sqrt{6}}{28\sqrt{3}}=\frac{3}{4}\sqrt{2}=\frac{3}{4}\times1.414=3\times0.3535=1.0605$$

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55 / 74

Choose the correct option.

$$\sqrt{\frac{.081\times.484}{.0064\times6.25}}$$ is equal to:

A0.9

B0.99

C9

D99

Explanation:

Sum of the decimal places in the numerator and denominator under the radical sign being the same, we remove the decimal.
Give exp. $$\sqrt{\frac{81\times484}{64\times625}}=\frac{9\times22}{8\times25}=0.99$$

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56 / 74

Choose the correct option.

$$\sqrt{\frac{(0.03)^2+(0.21)^2+(0.065)^2}{(0.003)^2+(0.021)^2+(0.0065)^2}}$$ is equal to:

A0.1

B10

C$$10^2$$

D$$10^3$$

Explanation:

Here is no explanation for this answer

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57 / 74

Choose the correct option.

The square root of $$(7+3\sqrt{5})(7-3\sqrt{5})$$ is:

A$$\sqrt{5}$$

B2

C4

D$$3\sqrt{5}$$

Explanation:

$$\sqrt{(7+3\sqrt{5})(7-3\sqrt{5})}=\sqrt{(7)^2-(3\sqrt{5})^2}=\sqrt{49-45}=\sqrt{4}=2$$

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58 / 74

Choose the correct option.

$$\left(\sqrt{3}-\frac{1}{\sqrt{3}}\right)^2$$ simplifies to:

A$$\frac{3}{4}$$

B$$\frac{4}{\sqrt{3}}$$

C$$\frac{4}{3}$$

DNone of these

Explanation:

$$\left(\sqrt{3}-\frac{1}{\sqrt{3}}\right)^2=(\sqrt{3})^2+\left(\frac{1}{\sqrt{3}}\right)^2-2\times \sqrt{3}\times \frac{1}{\sqrt{3}}$$
$$=3+\frac{1}{3}-2=1+\frac{1}{3}=\frac{4}{3}$$

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Choose the correct option.

If a=0.1039, then the value of $$\sqrt{4a^2-4a+1}+3a$$ is:

A0.1039

B0.2078

C1.1039

D2.1039

Explanation:

$$\sqrt{4a^2-4a+1}+3a=\sqrt{(1)^2+(2a)^2-2\times1\times2a}+3a$$
$$\sqrt{(1-2a)^2}+3a=(1-2a)+3a=(1+a)=(1+0.1039)=1.1039$$

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Choose the correct option.

The square root of $$\frac{(0.75)^3}{1-0.75}+[0.75+(0.75)^2+1]$$ is:

A1

B2

C3

D4

Explanation:

Here is no explanation for this answer

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