Updated By SaraNextGen
On March 11, 2024, 11:35 AM
Exercise 6.2 - Chapter 6 Square & Square Roots class 8 ncert solutions Maths - SaraNextGen [2024]
Question 1:
Find the square of the following numbers
(i) 32 (ii) 35
(iii) 86 (iv) 93
(v) 71 (vi) 46
Answer:
(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
Question 2:
Write a Pythagorean triplet whose one member is
(i) 6 (ii) 14
(iii) 16 (iv) 18
Answer:
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.
Also Read : Exercise-6.3-Chapter-6-Square-&-Square-Roots-class-8-ncert-solutions-Maths
