Question

Is 6125 a perfect cube? If not, by which smallest natural number should 6125 be divided so that the quotient is a perfect cube?

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given :-

The Number = 6125

To find :-

Is 6125 a perfect cube? If not, by which smallest natural number should 6125 be divided so that the quotient is a perfect cube?

Solution :-

Given number = 6125

It can be written as

6125 = 5×5×5×7×7

=> 6125 = (5×5×5)×(7×7)

6125 can not be written as the product of three same numbers.

6125 is not a perfect cube.

If we divide 6125 with (7×7) = 49 so that the quotient is a perfect cube

On dividing 6125 by 49

=> 6125/49

It can be written as

=> (5×5×5×7×7)/(7×7)

=> (5×5×5)

=> 125

=> 5³

Therefore, 5³ = 125 , a perfect cube.

Answer :-

1) 6125 is not a perfect cube.

2) 6125 should be divided by 49 so that the quotient is a perfect cube.

Used formulae:-

• A perfect cube is obtained by multiplying the number three times by itself.

• a³ = a×a×a