Square and Cube Roots Quiz Set 003

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Question 1

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

 A

${-7√11}/66$.

 B

${+7√11}/66$.

 C

${-11√7}/66$.

 D

${-18√11}/66$.

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 2

If $√2$ = 1.41, then what is the value of ${√2}/5$ − $11/{√2}$?

 A

-7.495.

 B

+7.495.

 C

-9.81.

 D

+9.81.

Soln.
Ans: a

The given expression can be simplified to ${{(√2)^2} - 5 × 11}/{5 × √2}$, which is same as ${2 - 55}/{5 × √2}$, which is same as ${-53/{5 × √2}$. Rationalizing, we get ${-53/{5 × √2} × {√2/√2}$ which gives ${-53√2}/10$ which = -7.495.


Question 3

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.


Question 4

What is the value of ${√11}/3$ − $2/{√11}$?

 A

${5√11}/33$.

 B

${15√11}/33$.

 C

${13√11}/33$.

 D

${6√11}/33$.

Soln.
Ans: a

The given expression can be simplified to ${{(√11)^2} - 3 × 2}/{3 × √11}$, which is same as ${11 - 6}/{3 × √11}$, which is same as ${5/{3 × √11}$. Rationalizing, we get ${5/{3 × √11} × {√11/√11}$ which gives ${5√11}/33$


Question 5

What is the value of $√{(13 - 3√5) × (13 + 3√5)}$?

 A

$√124$.

 B

$√248$.

 C

$√196$.

 D

$√416$.

Soln.
Ans: a

By inspection, we can easily see that the formula (a - b) × (a + b) can be used to simplify like this: $√{(13)^2 - (3√5)^2}$, which is same as $√{169 - (3^2 × 5)}$, which is same as $√{169 - 45}$ = $√124$.


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This Blog Post/Article "Square and Cube Roots Quiz Set 003" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer


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