Square and Cube Roots Quiz Set 020

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Question 1

What is the value of $(√4 - 1/√4)^2$?

 A

$2{1/4}$.

 B

$2{3/4}$.

 C

$2{1/3}$.

 D

$2{1/6}$.

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 = 4, we get ${9/4}$, which is same as: $2{1/4}$.


Question 2

What is the value of ${√11}/6$ − $3/{√11}$?

 A

${-7√11}/66$.

 B

${+7√11}/66$.

 C

${-3√11}/66$.

 D

${+3√11}/66$.

Soln.
Ans: a

The given expression can be simplified to ${{(√11)^2} - 6 × 3}/{6 × √11}$, which is same as ${11 - 18}/{6 × √11}$, which is same as ${-7/{6 × √11}$. Rationalizing, we get ${-7/{6 × √11} × {√11/√11}$ which gives ${-7√11}/66$


Question 3

What is cube root of 0.000343?

 A

0.07.

 B

.343

 C

0.007.

 D

0.700.

Soln.
Ans: a

We can see that 0.07 × 0.07 × 0.07 = 0.000343, so cube root is 0.07.


Question 4

What is the value of $√{3 + √1}$?

 A

2.

 B

√3.

 C

1.

 D

4.

Soln.
Ans: a

The given expression is same as $√{3 + √1^2}$, which becomes $√{3 + 1}$, or $√4$ which gives 2 as the answer. Please note that squares of as many numbers should be always on your tips.


Question 5

If x = 0.7968, then what is the value of $4x + √{16x^2 - 8x + 1}$?

 A

1.

 B

16.

 C

8.

 D

2.

Soln.
Ans: a

By inspection, $4x + √{16x^2 - 8x + 1}$ is same as $4x + √{({1 - 4x})^2}$, which is same as 4x + (1 - 4x) = 1.


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Creative Commons License
This Blog Post/Article "Square and Cube Roots Quiz Set 020" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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