NCERT Solutions for Class 8 Maths Chapter 5 Squares and Square Roots Ex 5.2
NCERT Solutions for Class 8 Maths Chapter 5 Squares and Square Roots Ex 5.2 are the part of NCERT Solutions for Class 8 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 8 Maths Chapter 5 Squares and Square Roots Ex 5.2.
Ex 5.2 Class 8 Maths Question 1.
Find the square of the following numbers.
(i) 32
(ii) 35
(iii) 86
(iv) 93
(v) 71
(vi) 46
Solution:
(i) 322 = (30 + 2)2
= 30 (30 + 2) + 2 (30 + 2)
= 302 + 30 × 2 + 2 × 30 + 22
= 900 + 60 + 60 + 4 = 1024
(ii) (35)2 = (30 + 5)2
= 30 (30 + 5) + 5 (30 + 5)
= 302 + 30 × 5 + 5 × 30 + 52
= 900 + 150 + 150 + 25 = 1225
(iii) (86)2 = (80 + 6)2
= 80 (80 + 6) + 6 (80 + 6)
= 802 + 80 × 6 + 6 × 80 + 62
= 6400 + 480 + 480 + 36 = 7396
(iv) (93)2 = (90 + 3)2
= 90 (90 + 3) + 3 (90 + 3)
= 902 + 90 × 3 + 3 × 90 + 32
= 8100 + 270 + 270 + 9 = 8649
(v) (71)2 = (70 + 1)2
= 70 (70 +1) +1 (70 +1)
= 702 + 70 × 1 + 1 × 70 + 12
= 4900 + 70 + 70 + 1 = 5041
(vi) (46)2 = (40 + 6)2
= 40 (40 + 6) + 6 (40 + 6)
= 402 + 40 × 6 + 6 × 40 + 62
= 1600 + 240 + 240 + 36 = 2116
Ex 5.2 Class 8 Maths Question 2.
Write a Pythagorean triplet whose one member is:
(i) 6
(ii) 14
(iii) 16
(iv) 18
Solution:
(i) Put m = 3 in 2m, m2 – 1, m2 + 1, we get
2m = 6, m2 – 1 = 32 – 1 = 9 – 1 = 8 and m2 + 1 = 9 + 1 = 10
Thus, 6, 8 and 10 are Pythagorean triplets.
(ii) Put m = 7 in 2m, m2 – 1, m2 + 1, we get
2m = 14, m2 – 1 = 72 – 1 = 49 – 1 = 48 and m2 + 1 = 72 + 1 = 49 + 1 = 50
Thus, 14, 48 and 50 are Pythagorean triplets.
(iii) Put m = 8 in 2m, m2 – 1, m2 + 1, we get
2m = 16, m2 – 1 = 82 – 1 = 64 – 1 = 63 and m2 + 1 = 82 + 1 = 64 + 1 = 65
Thus, 16, 63 and 65 are Pythagorean triplets.
(iv) Put m = 9 in 2m, m2 – 1, m2 + 1, we get
2m = 18, m2 – 1 = 92 – 1 = 81 – 1 = 80 and m2 + 1 = 92 + 1 = 81 + 1 = 82
Thus, 18, 80 and 82 are Pythagorean triplets.
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