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

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.