Question

find the smallest natural number by which 540 must be multiplied so that a square is a perfect cube​

Answer 1

Answer:

Step-by-step explanation:

First, factorize the number 540

2     |     540

2     |     270

3     |     135

3     |     45

3     |     15

5     |     5

     |     1

540 = 2² x 3³ x 5

For a perfect square, the powers of all factors must be divisible by 2.

Hence, 3 x 5 is required to be multiplied to the number so that the required factors are

(2² x 3³ x 5) x 3 x 5

= 2² x  x 5²

= 8100

Square root of the number can be calculated by dividing the power of each factor by 2

Square root = 2 x 3² x  5 = 90

Answer 2

Answer:

mark as brainliest answer

Step-by-step explanation:

The prime factorization of 540 is 22×33×51. Logically the answer would be 50. After all, 50=21×52 and 540×50 would then be

23×33×53=302.

But is 50 the smallest integer? Consider that 540×0=03 , and 0 is considerably less than 50. Zero is indeed an integer. Or how about −291600?

−291600×540=−5403

Even though it is negative, −291000 is still an integer and cubed numbers can be negative numbers. It is also considerably less than 50 or 0. In fact when you consider that negative numbers are integers, what really is the smallest possible integer that will make 540 a perfect cube? Thus the answer is unknown.