# Square and Cube Roots Quiz Set 020

### 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. 