Consider the following pattern. 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 Write 7 3 - 6 3 in the above pattern and find its value.

Let us observe the following pattern: 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 From the pattern, it appears that the relation a 3 - b 3 = 1 + a × b × 3 holds true for the pattern, a = b + 1 . Using the above relationship in the pattern, we shall use a = 7 and b = 6 for the expression 7 3 - 6 3 and write, 7 3 - 6 3 = 1 + 7 × 6 × 3 = 1 + 126 = 127 . Therefore, the required answer is 127 .

Consider the following pattern. 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 Write 12 3 - 11 3 in the above pattern and find its value.

Let us observe the following pattern: 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 From the pattern, it appears that the relation a 3 - b 3 = 1 + a × b × 3 holds true for the pattern, a = b + 1 . Using the above relationship in the pattern, we shall use a = 12 and b = 11 for the expression 12 3 - 11 3 and write, 12 3 - 11 3 = 1 + 12 × 11 × 3 = 1 + 396 = 397 . Therefore, the required answer is 397 .

Consider the following pattern. 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 Write 20 3 - 19 3 in the above pattern and find its value.

Let us observe the following pattern: 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 From the pattern, it appears that the relation a 3 - b 3 = 1 + a × b × 3 holds true for the pattern, a = b + 1 . Using the above relationship in the pattern, we shall use a = 20 and b = 19 for the expression 20 3 - 19 3 and write, 20 3 - 19 3 = 1 + 20 × 19 × 3 = 1 + 1140 = 1141 . Therefore, the required answer is 1141 .

Consider the following pattern. 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 Write 51 3 - 50 3 in the above pattern and find its value.

Let us observe the following pattern: 2 3 - 1 3 = 1 + 2 × 1 × 3 3 3 - 2 3 = 1 + 3 × 2 × 3 4 3 - 3 3 = 1 + 4 × 3 × 3 From the pattern, it appears that the relation a 3 - b 3 = 1 + a × b × 3 holds true for the pattern, a = b + 1 . Using the above relationship in the pattern, we shall use a = 51 and b = 50 for the expression 51 3 - 50 3 and write, 51 3 - 50 3 = 1 + 51 × 50 × 3 = 1 + 7650 = 7651 . Therefore, the required answer is 7651 .

E M B I B E

MATHEMATICS A TEXTBOOK FOR CLASS 8>Chapter 7 - Cubes and Cube Roots>TRY THESE

Jammu and Kashmir Board Solutions for Chapter: Cubes and Cube Roots, Exercise 4: TRY THESE

Author:Jammu and Kashmir Board

Jammu and Kashmir Board Mathematics Solutions for Exercise - Jammu and Kashmir Board Solutions for Chapter: Cubes and Cube Roots, Exercise 4: TRY THESE

Attempt the free practice questions on Chapter 7: Cubes and Cube Roots, Exercise 4: TRY THESE with hints and solutions to strengthen your understanding. MATHEMATICS A TEXTBOOK FOR CLASS 8 solutions are prepared by Experienced Embibe Experts.