SQUARE AND SQUARE ROOTS PRACTICE QUESTIONS

Problem 1 :

The value of √144 + √1.44 is ?

a. 24        b. 13.2       c. 1.32        d. none of these

Solution :

√144 + √1.44

√144 = √12 x 12

= 12

√1.44 = √1.44 x (100/100)

= √(144/100)

= √(12 x 12) /(10 x 10)

= 12/10

= 1.2

√144 + √1.44 = 12 + 1.2

= 13.2

Problem 2 :

Which of the following triplet is a Pythagorean Triplet:

a. (4, 5, 6)    b. (11, 60, 61)     c. (10, 8, 6)    d. both b and c

Solution :

Option a :

a = 4, b = 5 and c = 6

c² = a² + b²

6² = 4² + 5²

36 = 16 + 25

36 ≠ 41

So, option a is not Pythagorean triple.

Option b :

a = 11, b = 60 and c = 61

c² = a² + b²

61² = 11² + 60²

3721 = 121 + 3600

3721 = 3721

So, option b is Pythagorean triple.

Option c :

a = 10, b = 8 and c = 6

c² = a² + b²

10² = 8² + 6²

100 = 64 + 36

100 = 100

So, option c is Pythagorean triple.

Hence the correct answer is option d.

Problem 3 :

How many non square numbers are there in between 𝑛² 𝑎𝑛𝑑 (𝑛 + 1)²

a. 2n      b. 4n      c. 3n       d. 2n + 1

Solution :

There must be 2n natural numbers in between two consecutive numbers. So, the answer is option a.

Problem 4 :

The Simplified form of 

is

a. 30      b. 3     c. 10       d. None

Solution :

So, the answer is 10.

Problem 5 :

Evaluate √5² + 12²

Solution :

√5² + 12²

= √25 + 144

= √169

Problem 6 :

2707/√x = 27.07, find x.

Solution :

2707/√x = 27.07, find x.

Multiply by √x.

2707/√x = 27.07

Divide by 27.07 on both sides.

2707/27.07 = √x

100 = √x

Squaring both sides.

(100)² = x

x = 10000

So, the answer is 10000.

Problem 7 :

If √15625 = 125, then find the value of √156.25 + √1.5625

Solution :

√15625 = 125

= √156.25 + √1.5625

√156.25 + √1.5625 = 12.5 + 1.25

= 13.75

Problem 8 :

Find the square root of 14641 by prime factorisation method.

Solution :

√14641 = √(11 x 11 x 11 x 11)

= 11 x 11

= 121

Problem 9 :

Find the square root of 144 by repeated subtraction method

Solution :

After 12 steps, we get 0. So, square root of 144 is 12.

Problem 10 :

Is 2352 a perfect square? If not, find the smallest multiple of 2352 which is a perfect square. Find the square root of the new number.

Solution :

Factoring 2352 :

√2352 = √(2 x 2 x 2 x 2 x 7 x 7 x 3)

After grouping them as pairs, we find one 3 as extra. To group it, we need one more 3. So, 3 is the smallest number to be multiplied to make 2352 as perfect square.

Problem 11 :

Find the least number which should be subtracted from 180 to make it a perfect square.

Solution :

180 - 11 = 169

11 is the smallest number to be subtracted from 180 to make it as perfect square.