# Square Roots and Cube Roots Questions

Q:

The cube root of .000216 is:

 A) .6 B) .06 C) 77 D) 87

Explanation:

${\color{Blue}(.000216)&space;^{\frac{1}{3}}=\left&space;(&space;\frac{216}{10^{6}}&space;\right&space;)^{\frac{1}{3}}}&space;{\color{Blue}&space;=\left&space;[&space;\frac{6\times&space;6\times&space;6}{10^{2}\times&space;10^{2}\times&space;10^{2}}&space;\right&space;]^{\frac{1}{3}}}&space;{\color{Blue}&space;=\left&space;[&space;\frac{6}{10^{2}}&space;\right&space;]}&space;{\color{Blue}&space;=0.06}$

25 3947
Q:

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:

 A) 57 B) 67 C) 77 D) 87

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

${\color{Blue}&space;\therefore&space;}$  Number of members = ${\color{Blue}&space;\sqrt{5929}}$ = 77.

13 1263
Q:

If $\inline {\color{Black}\sqrt{0.00000676}=.0026}$ , the square root of 67,60,000 is:

 A) 2.6 B) 26 C) 260 D) 2600

Explanation:

$\inline {\color{Blue}\sqrt{6760000}=\sqrt{0.00000676\times 10^{2}}=\sqrt{0.00000676}\times \sqrt{10^{2}}=0.0026\times10 ^{6}=2600}$

16 1160
Q:

$\inline \fn_jvn {\color{Black}If \; x=(7-4\sqrt{3}),then\; the \; value\; of\; \left ( x+\frac{1}{x} \right )is:}$

 A) 3sqrt{3} B) 8sqrt{3} C) 14 D) 14+8sqrt{3}

Explanation:

$\inline \fn_jvn {\color{Blue} x+\frac{1}{x} =(7-4\sqrt{3})+\frac{1}{(7-4\sqrt{3})}\times \frac{(7+4\sqrt{3})}{(7+4\sqrt{3})}=(7-4\sqrt{3})+\frac{(7+4\sqrt{3})}{(49-48)}}$

$\inline \fn_jvn {\color{Blue} =(7-4\sqrt{3})+(7+4\sqrt{3})=14}$

25 821
Q:

$\inline \fn_jvn {\color{Black} \frac{3+\sqrt{6}}{5\sqrt{3}-2\sqrt{12}-\sqrt{32}+\sqrt{50}}=?}$

 A) 3 B) 3sqrt{2} C) 6 D) None of these

$\inline \fn_jvn {\color{Blue}Given\; exp.= \frac{3+\sqrt{6}}{5\sqrt{3}-4\sqrt{3}-4\sqrt{2}+5\sqrt{2}}=\frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}}$
$\inline \fn_jvn {\color{Blue}= \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\frac{3\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{3}}{3-2}=\sqrt{3}}$