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.

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