Square and Cube Roots Quiz Set 020

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Question 1

What is the value of $(√9 - 1/√9)^2$?

 A

$7{1/9}$.

 B

$7{2/3}$.

 C

$7{6/11}$.

 D

$7{11/81}$.

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 = 9, we get ${64/9}$, which is same as: $7{1/9}$.


Question 2

If $5√3 + √108 = 19.05$, then what is the value of $√27 + 3√3$?

 A

10.39.

 B

10.64.

 C

10.172.

 D

10.81.

Soln.
Ans: a

The given expression can be rearranged like this: $5√3 + √{6^{2} × 3}$, which is same as $5√3 + 6√3$ which is same as $11√3 = 19.05$, from which we get $√3 = 1.73$. Next we can see that $√27 + 3√3$ is same as $√{3^{2} × 3} + 3√3$, which is same as $6√3$, which gives $6 × 1.73$ = 10.39.


Question 3

If x = 0.8418, then what is the value of $4x + √{16x^2 - 8x + 1}$?

 A

1.

 B

8.

 C

32.

 D

16.

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.


Question 4

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

 A

${-15√3}/18$.

 B

${+15√3}/18$.

 C

${-9√3}/18$.

 D

${+9√3}/18$.

Soln.
Ans: a

The given expression can be simplified to ${{(√3)^2} - 6 × 3}/{6 × √3}$, which is same as ${3 - 18}/{6 × √3}$, which is same as ${-15/{6 × √3}$. Rationalizing, we get ${-15/{6 × √3} × {√3/√3}$ which gives ${-15√3}/18$


Question 5

If $√5$ = 2.24, then what is the value of ${√5}/2$ − $9/{√5}$?

 A

-2.907.

 B

-2.073.

 C

-2.007.

 D

-2.097.

Soln.
Ans: a

The given expression can be simplified to ${{(√5)^2} - 2 × 9}/{2 × √5}$, which is same as ${5 - 18}/{2 × √5}$, which is same as ${-13/{2 × √5}$. Rationalizing, we get ${-13/{2 × √5} × {√5/√5}$ which gives ${-13√5}/10$ which = -2.907.


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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 2017-10-26.

Posted by Parveen(Hoven),
Aptitude Trainer


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