# Square and Cube Roots Quiz Set 003

Advertisement

 Correct Answers: Wrong Answers: Unattempted:

### 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\$.

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

Advertisement