Question 1

Which of the following numbers, Where in some of the digit have been suppressed by Symbols, can possibly be the perfect square of a 3 digit odd number.?

Accepted Answer

The square of an odd number cannot have 4 as the unit digit. The square of a 3 digit number will have at least 5 digit and at the most 6 digits. So. answer (A) is correct.

Question 2

√ 0.04 x 0.4 x a = 0.4 x 0.04 x √ b, then the value of a/b is?

Accepted Answer

√0.04 x 0.4 x a = 0.4 x 0.04 x √b ⇒ √0.016 a = 0.016 x √b ⇒ √a / √b = 0.016/√0.016 = √0.016 ∴ √a/b = √0.016 So a/b = 0.016

Question 3

The least perfect square number divisible by 3, 4, 5, 6, 8 is?

Accepted Answer

L. C. M of 3, 4, 5, 6, 8 is 120 Now, 120 = 2 x 2 x 2 x 3 x 5 ∴ Required number = (2 x 2 x 2 x 3 x 5) x (2 x 3 x 5) = 3600

Question 4

(√ 5 - √ 3)/ (√ 5 + √ 3) is equal to?

Accepted Answer

(√5 - √3)/ (√5 + √3) = (√5 - √3) / (√5 + √3) = (√5 - √3)2 / (5 - 3) = (5 + 3 - 2√5 x 3) / 2 = 2 (4 - √15) / 2 = (4 - √15)

Question 5

If a = (√ 5 + 1) / (√ 5 - 1) and b = (√ 5 - 1) / ( √ 5 + 1) then the value of (a 2 + ab + b 2) / (a 2 - ab + b 2) is?

Accepted Answer

a = [(√5 + 1) / (√5-1)] x [(√5 + 1) / (√5 + 1)] = (√5 + 1)2 / (5 - 1) = (5 + 1 + 2 √5) / 4 = (3 + √5) / 2 b = [(√5 - 1) / (√5 + 1)] x [(√5 - 1 ) / (√5 -1)] = (√5 - 1 )2 / (5 - 1) = (5 + 1 - 2√5) / 4 = (3 - √5) / 2 Now a2 + b2 = [(3 + √5)2 + (3 - √5)2] / 4 = [2 x (9 + 5 )] / 4 = 7 ab = 1 ∴ (a2 + ab + b2) / (a2 - ab + b2) = (7 + 1) / (7 - 1) = 8/6 = 4 / 3

Question 6

The least number by which 216 must be divided to make the result a perfect square is?

Accepted Answer

216 = 2 x 2 x 2 x 3 x 3 x 3 = (2 x 2) x 2 x ( 3 x 3) x 3 Clearly, in order to make it a perfect square, it must be divided by 2 x 3 i.e., 6 .

Question 7

The least number by which 176 be multiplied to make the result a perfect square is?

Accepted Answer

176 = 2 x 2 x 2 x 2 x 11 So, in order to make it a perfect square, it must be multiplied by 11.

Question 8

The length of diagonal of a square is 8 cm. The length of the side of the square is?

Accepted Answer

a2 + a2 = (8)2 ⇒ 2a2 = 64 ⇒ a2 = 32 ∴ a = √32 = 4√2 = 4 x 1.41 = 5.64 cm

Question 9

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 22.09, the number of members in the group is?

Accepted Answer

Number of members = √2209 = 47

Question 10

The square root of (1/4) x (1/49) ÷ (25/121) is

Accepted Answer

Square root of (1/4) x (1/49) ÷ (25/121) = √(1/4) x (1/49) x (121/25) = 11 / (2 x 7 x 5) = 11/70

Question 11

A certain number of people agree to subscribe as many rupees each as a there are subscribers. The whole subscription is 2582449 rupees. Find the number of subscribers.

Accepted Answer

Let the total number of subscribers be x. Then, according to the question, x2 = 2582449 ∴ x = √2582449 = 1607

Question 12

Find the least number by which 175760 be devided to make it a perfect cube.

Accepted Answer

175760 = 24 x 5 x 13 3 = 23 x 2 x 5 x 133 To make perfect cube, it must be divided by 2 x 5 = 10

Question 13

The student of class XI of a school donated 4356 Rupees in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Accepted Answer

Total money donated = 4356 rupees As total students are equal to the sum donated by each student. Total Students =√4356 = 66

Question 14

If √ 256 / √ x = 2, then x is equal to?

Accepted Answer

√256 / √x = 2 ⇒ 16 = 2√x ⇒ √x = 8 ∴ x = 64.

Question 15

If N = 11 9/ 16 then √ N =?

Accepted Answer

N = 25/16 ∴ √N = √25/16 = 5/4 = 11/4

Question 16

If √ 2401 = √ 7x then, the value of x is?

Accepted Answer

√2401 = √7x ⇒ 7x = 2401 = 74 ∴ x = 4

Question 17

What is the smallest number by which 3600 be divided to make it a perfect cube?

Accepted Answer

3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5. To make it a perfect cube, the given number must be divided by 2 x 3 x 3 x 5 x 5 = 450

Question 18

By what least number must 21600 be multiplied to make it a perfect cube?

Accepted Answer

21600 = 6 x 6 x 6 x 10 x 10 To, make the given number a perfect cube, it must be multiplied by 10.

Question 19

The sequence root of 0. 4 is

Accepted Answer

√0.4 = √4/9 = 2/3 = 0.666 = 0.6

Question 20

Find the square root of 105 4/ 64.

Accepted Answer

√1054/64 = √6724/64 = 82/8 = 41/4 = 101/4

Square Root and Cube Root Questions