Question

find the smallest number by which 289 must be multiplied to obtain a perfect cube?also find the cube root of the number so obtained​

Answer 1

Answer:

Step-by-step explanation:

(v) 7803

First find the prime factors of 7803

7803 = 3 × 3 × 3 × 17 × 17

= 33 × 172

Since 7803 is not a perfect cube.

To make the quotient a perfect cube we divide it by 17^2 = 289, which gives 27 as quotient and we know that 27 is a perfect cube

∴ 289 is the required smallest number.