# Square Roots and Cube Roots Question & Answers

## Square Roots and Cube Roots

Quantitative aptitude questions are asked in many competitive exams and placement exam. "Square Root and Cube Root" is a category in Quantitative Aptitude. Quantitative aptitude questions given here are extremely useful for all kind of competitive exams like Common Aptitude Test (CAT), MAT, GMAT, IBPS Exam, CSAT, CLAT, Bank Competitive Exams, ICET, UPSC Competitive Exams, CLAT, SSC Competitive Exams, SNAP Test, KPSC, XAT, GRE, Defense Competitive Exams, L.I.C/ G. I.C Competitive Exams, Railway Competitive Exam, TNPSC, University Grants Commission (UGC), Career Aptitude Test (IT Companies) and etc., Government Exams etc.

We have a large database of problems on "Square Root and Cube Root" answered with explanation. These will help students who are preparing for all types of competitive examinations.

The cube root of .000216 is:

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

Explanation:

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

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

17

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.

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

10

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:

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

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

12

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

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

Explanation:

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

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

Subject: Square Roots and Cube Roots - Quantitative Aptitude - Arithmetic Ability

22

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

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

Explanation:

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

$\inline \fn_jvn {\color{Blue}= \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\frac{3\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{3}}{3-2}=\sqrt{3}}$