# Square and Cube Roots Quiz Set 004

### 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.