NCERT Solutions for class 8 Maths chapter 6 Square and square roots exercise 6.2

Exercise 6.2

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Q 1 - Ex 6.2 - Square and Square Roots - NCERT Maths Class 8th - Chapter 6

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Question 1
Find the square of the following numbers
(i) 32 (ii) 35
(iii) 86 (iv) 93
(v) 71 (vi) 46
Sol :
(i) 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. Therefore,
35² = (3) (3 + 1) hundreds + 25
= (3 × 4) hundreds + 25
= 1200 + 25 = 1225
(iii) 86² = (80 + 6)²
= 80 (80 + 6) + 6 (80 + 6)
= 80² + 80 × 6 + 6 × 80 + 6²
= 6400 + 480 + 480 + 36
= 7396

(iv) 93² = (90 + 3)²
= 90 (90 + 3) + 3 (90 + 3)
= 90² + 90 × 3 + 3 × 90 + 3²
= 8100 + 270 + 270 + 9
= 8649

(v) 71² = (70 + 1)²
= 70 (70 + 1) + 1 (70 + 1)
= 70² + 70 × 1 + 1 × 70 + 1²
= 4900 + 70 + 70 + 1
= 5041

(vi) 46² = (40 + 6)²
= 40 (40 + 6) + 6 (40 + 6)
= 40² + 40 × 6 + 6 × 40 + 6²
= 1600 + 240 + 240 + 36
= 2116

Q 2 - Ex 6.2 - Square and Square Roots - NCERT Maths Class 8th - Chapter 6

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Question 2
Write a Pythagorean triplet whose one member is
(i) 6 (ii) 14
(iii) 16 (iv) 18
Sol :
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
Again 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
The value of m will not be an integer.
If we take m² − 1 = 14, then m² = 15
Again 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 required triplet is 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.
Let 2m = 16
m = 8
Thus, m² − 1 = 64 − 1 = 63 and m² + 1 = 64 + 1 = 65
Therefore, the Pythagorean triplet is 16, 63, and 65.

(iv) If we take m² + 1 = 18,
m² = 17
The value of m will not be an integer.
If we take m² − 1 = 18, then m² = 19
Again the value of m is not an integer.
Let 2m =18
m = 9
Thus, m² − 1 = 81 − 1 = 80 and m² + 1 = 81 + 1 = 82
Therefore, the Pythagorean triplet is 18, 80, and 82.