# Squares and Square Roots| Worksheet Solutions| Class 8

Worksheet solutions for chapter: Squares and Square Roots for class 8 are provided below.

(1) Express 169 as the sum of 13 odd numbers.

Ans-

Successively subtract odd numbers from 169

(a) 169 – 1 = 168

(b) 168 – 3= 165

(c) 165 – 5 = 160

(d) 160 – 7 = 153

(e) 153– 9 = 144

(f) 144 – 11= 133

(g) 133 – 13 = 120

(h)120 – 15= 105

(i) 105 – 17 = 88

(j) 88 – 19 = 69

(k) 69 – 21 = 48

(l) 48 – 23 =25

(m) 25 – 25 = 0

Hence,169 can be express as the sum of 13 odd numbers =

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25

(2) How many numbers lie between squares of the 24 and 25.

Ans-

24 and 25

Square of 25 = 625

Square of 24 = 576

Difference of square of numbers = 625 – 576 = 49

Non squares numbers between two square numbers is one less than the difference between squares of those two consecutive numbers.

Non squares numbers between two square numbers

= Difference of square of numbers – 1

= 49 -1

= 48

Hence, non square numbers between squares of 24 and 25 are 48.

(3) Find the square of the 77 number.

Ans-

77 can be written as (70 +7)

77 =70 + 7

772 = (70 + 7)2

= (70 + 7) (70 + 7)

= 70(70 + 7) + 7(70 + 7 )

= 70 × 70 + 70 ×7 + 7× 70 + 7×7

= 4900 + 490 + 490 + 49

= 5929

Hence, square of 77 is 5929.

(4) Write a Pythagorean triplet whose one number is 8.

Ans- (5) Find the square root of 289 by the method of repeated subtraction.

Ans-

289

Successively subtract odd numbers from 169

(a) 289 – 1 = 288

(b) 288 – 3= 285

(c) 285 – 5 = 280

(d) 280 – 7 = 273

(e) 273 – 9 = 264

(f) 264 – 11= 253

(g) 253 – 13 = 240

(h) 240 – 15= 225

(i) 225– 17 = 208

(j) 208 – 19 = 189

(k) 189 – 21 = 168

(l) 168 – 23= 145

(m) 145 – 25 =120

(n) 120 – 27 = 93

(o) 93 – 29 = 64

(p) 64 – 31=33

(q) 33 – 33 = 0

289 can be express as the sum of 17 odd numbers

= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19+21 + 23 + 25 + 27 + 29 + 31 + 33

Hence, square root of 169 = 17

(6) Find the square roots of the 324 by the Prime Factorisation Method.

Ans-

324  (7) Find the smallest whole number by which number 600 should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

Ans-

600  (8) Find the square root of the number 3136 by the Division Method.

Ans-

Square root of 3136 by division method is showing below:  (9) Find the square root of the 2.89.

Ans-

Square root of 2.89 by division method is showing below:  (10) Find the least number which must be added to 6172 to get a perfect square. Also find the square root of the perfect square so obtained.

Ans-

6172

Square root of the 6172 by division method is shown below:  Helping Topics

Squares and Square Roots

NCERT Solutions Class 8