Question

What is the smallest number by which 35721 must be multiplied so thar the product is perfect cube

Answer 1

Answer:

7

Step-by-step explanation:

by taking l.c.m. of the number we come to know that we should multiply 7 to the number

Answer 2

Answer:

Required smallest digit is 7.

Step-by-step explanation:

Given digit is 35721.

Here we want to find the smallest number by which 35721 must be multiplied so thar the product is perfect cube.

For solving this question,we need to prime factorisation of 35721.

$35721 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 7 \times 7$

We can write,

$35721 = {3}^{3} \times {3}^{3} \times {7}^{2}$

Here if power of 7 will be 3 then 35721 will be become perfect cube.So we need to multiply 7 to 35721 for perfect cube digit

Therefore, required smallest number is 7.

Some important cube value-

${1}^{3} = 1 \\ {2}^{3} = 8 \\ {3}^{3} = 27 \\ {4}^{3} = 64 \\ {5}^{3} = 125 \\ {6}^{3} = 216 \\ {7}^{3} = 343 \\ {8}^{3} = 512 \\ {9}^{3} = 729 \\ {10}^{3} = 1000$