Question

Find the least number by which 576 should be multiplied to get a perfect cube:

Answer 1

Answer:

BY MULTIPLYING 576 BY 3 IT GIVES THE ANS AS 1728 WHICH IS A PERFECT SQUARE OF 12.

Answer 2

• The required least number is equal to 3 .

To Find :- The least number by which 576 should be multiplied to get a perfect cube ?

Concept used :-

• For a number to be perfect cube, its each prime factor must be in pair of three .

Solution :-

Finding prime factors of 576 we get,

→ 576 ÷ 2 = 288

→ 288 ÷ 2 = 144

→ 144 ÷ 2 = 72

→ 72 ÷ 2 = 36

→ 36 ÷ 2 = 18

→ 18 ÷ 2 = 9

→ 9 ÷ 3 = 3

→ 3 ÷ 3 = 1

So,

→ 576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

now, writing prime factors of 576 in pair of three we get,

→ 576 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3)

as we can see that, both prime factors 2 is in pair of three but prime factor 3 is in pair of two only .

therefore, we can conclude that, in order to make the number a perfect cube we must multiply 576 by 3 both sides, so that, in RHS we have prime factor 3 also becomes in pair of three .

→ 576 × 3 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) .

hence, the least number by which 576 should be multiplied to get a perfect cube is equal to 3 .

Extra :-

→ Required perfect cube number = 576 × 3 = 1728

and,

→ Cube root of required number = 2 × 2 × 3 = 12 .

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