# Square and Cube Roots Quiz Set 010

### Question 1

If x = 0.6877, then what is the value of \$8x + √{25x^2 - 10x + 1}\$?

A

3.06.

B

2.16.

C

4.16.

D

3.64.

Soln.
Ans: a

By inspection, \$8x + √{25x^2 - 10x + 1}\$ is same as \$8x + √{({1 - 5x})^2}\$, which is same as 8x + (1 - 5x) = 1 + 3x = 3.06.

### Question 2

What is √(378) × √(6048)?

A

1512.

B

1496.

C

1440.

D

1500.

Soln.
Ans: a

We can see that √(378) × √(6048) is same as √(2 × 3 × 3 × 3 × 7 ) × √(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 ) which equals √(26 × 36 × 72), which equals (23 × 33 × 71), which gives 1512.

### Question 3

What is the value of \$x\$ in \$√{0.0196 × x}\$ = 1.4?

A

100.

B

0.0014.

C

96.

D

128.

Soln.
Ans: a

The given expression can be simplified to \$0.0196 × x\$ = \$1.4^2\$, which gives x = \${1.4^2}/0.0196\$, which is same as \$1.96/0.0196\$ which gives 100.

### Question 4

What is the value of \$x\$ in \$√{0.0016 × x}\$ = 0.4?

A

100.

B

10.

C

1.

D

1000.

Soln.
Ans: a

The given expression can be simplified to \$0.0016 × x\$ = \$0.4^2\$, which gives x = \${0.4^2}/0.0016\$, which is same as \$0.16/0.0016\$ which gives 100.

### Question 5

What is the value of \$√{3 + √1089}\$?

A

6.

B

3.

C

12.

D

9.

Soln.
Ans: a

The given expression is same as \$√{3 + √33^2}\$, which becomes \$√{3 + 33}\$, or \$√36\$ which gives 6 as the answer. Please note that squares of as many numbers should be always on your tips. 