Square and Cube Roots Quiz Set 004

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Question 1

What is the value of $(√2 - 1/√2)^2$?

 A

${1/2}$.

 B

${1/4}$.

 C

${2/3}$.

 D

${2/5}$.

Soln.
Ans: a

I will give a general solution for any n. $(√n - 1/√n)^2$ is same as $({(√n)^2 - 1}/√n)^2$ which becomes $(n - 1)^2/n$. Putting n = 2, we get ${1/2}$.


Question 2

One-half of the cube-root of which number is 0.3?

 A

0.216.

 B

0.256.

 C

0.128.

 D

0.144.

Soln.
Ans: a

Let the number be n. So ${1/2} × √^3n$ = 0.3, which gives $√^3n$ = 2 × 0.3 = 0.6. so n = $0.6^3$ = 0.216.


Question 3

If $2√3 + √108 = 13.86$, then what is the value of $√108 + 6√3$?

 A

20.78.

 B

20.18.

 C

20.16.

 D

20.96.

Soln.
Ans: a

The given expression can be rearranged like this: $2√3 + √{6^{2} × 3}$, which is same as $2√3 + 6√3$ which is same as $8√3 = 13.86$, from which we get $√3 = 1.73$. Next we can see that $√108 + 6√3$ is same as $√{6^{2} × 3} + 6√3$, which is same as $12√3$, which gives $12 × 1.73$ = 20.78.


Question 4

What is the value of ${√5}/3$ − $5/{√5}$?

 A

${-10√5}/15$.

 B

${+10√5}/15$.

 C

${-9√5}/15$.

 D

${+9√5}/15$.

Soln.
Ans: a

The given expression can be simplified to ${{(√5)^2} - 3 × 5}/{3 × √5}$, which is same as ${5 - 15}/{3 × √5}$, which is same as ${-10/{3 × √5}$. Rationalizing, we get ${-10/{3 × √5} × {√5/√5}$ which gives ${-10√5}/15$


Question 5

What is the value of ${√1296/5}$ × ${6/√36}$ × ${5/√36}$?

 A

6.

 B

30.

 C

36.

 D

144.

Soln.
Ans: a

The given expression can be simplified to ${√6^4/5}$ × ${6/√6^2}$ × ${5/√6^2}$, which is same as ${6^2/5}$ × ${6/6}$ × ${5/6}$, which cancels to 6.


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This Blog Post/Article "Square and Cube Roots Quiz Set 004" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-10-26.

Posted by Parveen(Hoven),
Aptitude Trainer


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