Question

what is the smallest number by which 1372 must be multiplied so that the product become a perfect cube? find the required perfect cube so obtained.​

Answer 1

Answer:

Step 1 : We will find the prime factors of 1372 by prime factorisation method

$1372 = 2 \times 2 \times 7 \times 7 \times 7$

Step 2 : Find the least number

If we , the prime factors of 1372 , 7 is in the group of 3 i.e . It make a cube but 2 is not in a group of 3 i.e. It is not making a cube .

= 2 is the smallest number by which 1372 must be multiplied so that the product become a perfect cube .

1372 X The least number .

$= 1372 \times 2 \\ = 2744 \\ = \sqrt{2744} = 14$

Hope it will help you

Answer 2

Answer:

Step 1: We will find the prime factors of 1372

by prime factorisation method

1372 = 2 × 2 × 7 × 7 × 7

Step 2: Find the least number

If we see, the prime factors of 1372, 7 is in

the group of 3 i.e. it makes a cube but 2 is

not in a group of 3 i.e. it is not making a

cube.

•2 is the smallest number by which 1372 must be multiplied so that the product becomes a perfect cube.

Let's check:

→1372 x The least number

⇒1372 × 2

⇒ 2744

→$\sqrt[3]{2744 } = 14$

Hence, proved.