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# Square Root and Cube Root Questions

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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:

$$\sqrt{4a2 - 4a + 1} + 3a = \sqrt{(1)^2 + (2a)^2 - 2 x 1 \times 2a }+ 3a$$

= $$\sqrt{(1 - 2a)^2} + 3a$$

= (1 - 2a) + 3a

= (1 + a)

= (1 + 0.1039)

= 1.1039

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Choose the correct option.

If $$x = \frac{\sqrt3 + 1}{\sqrt3-1}$$ and $$y = \frac{\sqrt3 - 1}{\sqrt3+1}$$ , then the value of $$(x^2 + y^2)$$ is:

A10

B13

C14

D15

Explanation:

$$x =\frac{(\sqrt3 + 1)}{(\sqrt3-1)} \times\frac{(\sqrt3 + 1)}{(\sqrt3+1)}= \frac{(\sqrt3 + 1)^2}{3-1} = \frac{3 + 1 + 2\sqrt3}{2} = 2 +\sqrt 3.$$

$$y = \frac{(\sqrt3 - 1)}{(\sqrt3+1)} \times \frac{(\sqrt3 - 1)}{(\sqrt3-1)}= \frac{(\sqrt3 - 1)^2}{3-1} = \frac{3 + 1 - 2\sqrt3}{2} = 2 -\sqrt 3.$$

$$x^2 + y^2 = (2 + \sqrt3)^2 + (2 - \sqrt3)^2$$ = 2(4 + 3) = 14

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Choose the correct option.

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

A57

B67

C77

D87

Explanation:

Money collected = $$(59.29 \times 100)$$ paise = 5929 paise.

Number of members$$=\sqrt 5929 = 77.$$

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Choose the correct option.

The square root of$$(7 + 3\sqrt5) (7 - 3\sqrt5)$$ is

A$$\sqrt5$$

B2

C4

D$$3\sqrt5$$

Explanation:

$$\sqrt{(7 + 3\sqrt5)(7 - 3\sqrt5) } = \sqrt{(7)^2 - (3\sqrt5)^2} =\sqrt{ 49 - 45 } = \sqrt4 = 2$$.

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If $$\sqrt5 = 2.236$$, then the value of $$\frac{\sqrt5}{2} - \frac{10}{\sqrt5} +\sqrt{125}$$ is equal to:

A5.59

B7.826

C8.944

D10.062

Explanation:

$$\frac{\sqrt5}{2} - \frac{10}{\sqrt5} + \sqrt{125} = \frac{(\sqrt5)^2 - 20 + 2\sqrt5 \times 5\sqrt5}{2\sqrt5}$$

= $$\frac{5 - 20 + 50}{2\sqrt5}$$

= $$\frac{35}{2\sqrt5} \times \frac{\sqrt5}{\sqrt5}$$

= $$\frac{35\sqrt5}{10}$$

= $$\frac{7 \times2.236 }{2}$$= 7 x 1.118= 7.826

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Choose the correct option.

$$\left( \frac{\sqrt{625}}{11} \times \frac{14}{\sqrt{25}} \times \frac{11}{\sqrt{196}} \right)$$ is equal to:

A5

B6

C8

D11

Explanation:

Given Expression = $$\frac{25}{11} \times \frac{14}{5} \times\frac{11}{14}= 5$$.

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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, $$0.0169x = (1.3)^2 = 1.69$$

$$\Rightarrow x = \frac{1.69}{0.0169} = 100$$

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Choose the correct option.

Simplifies the below expression:
$$\left( \sqrt{3} - \frac{1}{\sqrt{3}}\right)^{2}$$

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

B$$\frac{4}{\sqrt3}$$

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

Dnone of these

Explanation:

$$\left(\sqrt3 - \frac{1}{\sqrt3}\right)^2=(\sqrt3)^2 +\left( \frac{1}{\sqrt3}\right)^2 -2\times\sqrt 3\times \frac{1}{\sqrt3}$$
$$=3+\frac{1}{3}-2 =1 +\frac{1}{3}=\frac{4}{3}$$

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How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8 ?

A1

B2

C3

DNone of these

Explanation:

A number ending in 8 can never be a perfect square.

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Choose the correct option.

The square root of 64009 is:

A253

B347

C363

D803

Explanation:

Here is no explanation for this answer

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