Question

By what number should 40500 be multiplied to obtain a perfect cube?

Answer 1

Answer: 18

Step-by-step explanation:

Write the prime factorization of the number

40500=2*2*5*5*5*3*3*3*3

Now make group of three as we want perfect cube

5,5,5. 3,3,3.

Now write number left. 3,2,2

So to make group of three for these numbers we need 1 "2" and 2 "3"

Thus answer is 2*3*3

That is 18

Answer 2

18 should multiplied to 40500 to get perfect cube that is 729000.

Solution:

We need to determine what number should be multiplied to 40500 to obtain a perfect cube.

Let’s first do prime factorization of 40500

40500 = 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 x 5

$=2^{2} \times 3^{3} \times 3 \times 5^{3}$

For perfect cube we need all the powers must be 3.

So if we multiply one 2 and two threes on both side we get

$40500 \times 2 \times 3 \times 3=2^{3} \times 3^{3} \times 3^{3} \times 5^{3}$

So we get 40500 x 18 = 729000 and cube root of 729000 = 2 x 3 x 3 x 5 = 90.

Hence 18 should be multiplied to 40500 to get perfect cube that is 729000.