Class 8 CBSE Mathematics Guide - Chapter 6, Squares and Square Roots - NCERT Exercise 6.2 Solved

Class 8, CBSE (NCERT) Mathematics

Chapter 6, SQUARES AND SQUARE ROOTS - Mathematics Exercise 6.2

(CBSE Guide - NCERT Solutions)

(Page 98)

Question.1: Find the square of the following numbers

(i) 32 (ii) 35

(iii) 86 (iv) 93

(v) 71 (vi) 46

Solutions:

(i) 32 = (30 + 2)

=> 32² = (30 + 2)²

=> 30 (30 + 2) + 2 (30 + 2)

=> 30² + 30 × 2 + 2 × 30 + 2²

=> 900 + 60 + 60 + 4

=> 1024

(ii) The number 35 has 5 in its unit’s place.

Hence, 35² = (3) (3 + 1) hundreds + 25

=> (3 × 4) hundreds + 25

=> 1200 + 25

=> 1225

(iii) 86 = 80 + 6

=> 86² = (80 + 6)²

=> 80 (80 + 6) + 6 (80 + 6)

=> 80² + 80 × 6 + 6 × 80 + 6²

=> 6400 + 480 + 480 + 36

=> 7396

(iv) 93 = (90 + 3)

=> 93² = (90 + 3)²

=> 90 (90 + 3) + 3 (90 + 3)

=> 90² + 90 × 3 + 3 × 90 + 3²

=> 8100 + 270 + 270 + 9

=> 8649

(v) 71 = (70 + 1)

=> 71² = (70 + 1)²

=> 70 (70 + 1) + 1 (70 + 1)

=> 70² + 70 × 1 + 1 × 70 + 1²

=> 4900 + 70 + 70 + 1

=> 5041

(vi) Taking hint from above solutions, try to solve it yourself.

Question.2: Write a Pythagorean triplet whose one member is

(i) 6 (ii) 14

(iii) 16 (iv) 18

Solutions: We know that for any natural number m > 1, 2m, m² − 1, m² + 1 forms a Pythagorean triplet.

(i) If we take m² + 1 = 6, then m² = 5

The value of m will not be an integer.

If we take m² − 1 = 6, then m² = 7

Also, the value of m is not an integer.

Let 2m = 6

=> m = 3

Therefore, the Pythagorean triplets are 2 × 3, 3² − 1, 3² + 1 or 6, 8, and 10.

(ii) If we take m² + 1 = 14, then m² = 13

Clearly, m will not be an integer.

If we take m² − 1 = 14, then m² = 15

Also, the value of m is not an integer.

Let 2m = 14

=> m = 7

Thus, m² − 1 = 49 − 1 = 48 and m² + 1 = 49 + 1 = 50

Therefore, the Pythagorean triplets are 14, 48, and 50.

(iii) If we take m² + 1 = 16, then m² = 15

The value of m will not be an integer.

If we take m² − 1= 16, then m² = 17

Again the value of m is not an integer.

Say, 2m = 16

=> m = 8

Thus, m² − 1 = 64 − 1 = 63 and m² + 1 = 64 + 1 = 65

Therefore, the Pythagorean triplets are 16, 63, and 65.

(iv) Taking hint from above solutions try to solve it yourself.