GSEB Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.2

Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.2 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.2

Question 1.
Find the square of the following numbers containing 5 in unit place?

  1. 32
  2. 35
  3. 86
  4. 93
  5. 71
  6. 46

Solution:
1. (32)2 = (30 + 2)2
= 302 + 2(30)(2) + (2)2
= 900 + 120 + 4 = 1024

2. (35)2 = (30 + 5)2
= (30)2 + 2(30)(5) + (5)2
= 900 + 300 + 25
= 1200 + 25 = 1225

Second method
352 = 3 × (3 + 1) × 100 + 25
= 3 × 4 × 100 + 25
= 1200 + 25 = 1225

3. (86)2 = (80 + 6)2
= (80)2 + 2(80)(6) + (6)2
= 6400 + 960 + 36 = 7396

4. (93)2 = (90 + 3)2
= (90)2 + 2(90)(3) + (3)2
= 8100 + 540 + 9 = 8649

5. (71)2 = (70 + 1)2
= (70)2 + 2(70)(1) + (1)2
= 4900 + 140 + 1 = 5041

6. (46)2 = (40 + 6)2
= (40)2 + 2(40)(6) + (6)2
= 1600 + 480 + 36
= 2116

GSEB Solutions Class 8 Maths Chapter 6 Square and Square Roots Ex 6.2

Question 2.
Write a Pythagorean tripler whose one member is

  1. 6
  2. 14
  3. 16
  4. 18

Solution:
1. Let 2n – 6 ∴ n = 3
Now, n2 – 1 = 32 – 1 = 8
and n2 + 32 + 1 = 10
Thus, the required Pythagorean triplet is 6, 8, 10.

2. Let 2n = 14 ∴ n = 7
Now, n2 – 1 = 72 – 1 = 48
and n2 + 1 = 72 + 1 = 50
Thus, the required Pythagorean triplet is 14, 48, 50.

3. Let 2n = 16 ∴ n = 8
Now n2 – 1
= 64 – 1 = 63
and n2 + 1 = 82 + 1
= 64 + 1
= 65
∴ The required Pythagorean triple (is 16, 63, 65)

4. Let 2n = 18
Now, n2 – 1 = 92 – 1
= 81 – 1 = 80
and n2 + 1 = 92 + 1
= 81 + 1 = 82
The required Pythagorean triplet is 18, 80, 82.

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