You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Class 8

You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Class 8

Question 1.

You are told that 1331 is a perfect cube. Can you guess without factorisation what its cube root is? Similarly, guess the cube roots of 4913,12167, and 32768. Class 8

Solution:

Cube root of 1331 = 11, cube root of 4913 = 17, cube root of 12167 = 23 and cube root of 32768 = 32.

Question 2.

Which of the following is the greatest? Explain your reasoning. Class 8

(i) 67³ - 66³

(ii) 43³ - 42³

(iii) 67² - 66²

(iv) 43² - 42²

Solution:

(i) 67³ - 66³ is the greatest, because it can be expressed as (67 - 66) (67² + 66² + 67 × 66) = 1 × (67² + 66² + 67 × 66)

43³ - 42³ = 1 × (43² + 42² + 43 × 42), 67² - 66² = 1 × (67 + 66) and 43² - 42² = 1 × (43 + 42).