Question

............
15 points


Find the smallest number by which by 2025 must be
multiplied to make a perfect cube. Also find the cube root
of the number thus obtained.​

Answer 1

Answer:

here we have 4116 = 2² x 1029

=> 2² x 7³ x 3

Thus to make a perfect cube

we need to multiply the number by 2 x 3² = 18

Answer 2

To Find :-

• smallest number by which by 2025 must be
• multiplied to make a perfect cube ?

Answer :-

Prime factorization of 2025 :-

2025 = 5² * 9²

Here, for making the product perfect cube, above number needs minimum one more 5 and one more 9.

So that, every factor has exponent 3...

So, the given number is to be multiplied by = 5 * 9 = 45

Hence, 2025 is Multiply by 45 to Make Perfect Cube...

And,

→ 2025 * 45 = 5³ * 9³

so,

→ Cube Root = 5 * 9 = 45 .

Hence, the cube root of the number thus oobtained is Also 45..