Question

Smallest natural number by which the number 405 must be multiplied to make it a perfect square

Answer 1

405=3×3×3×3×5 as we can see if we root 405,two 3's will come out but one 5 will remain so we need one more 5 so multiply by 5

Answer 2

----------------------------------------

Here is the solution:

----------------------------------------

Find the prime factors of 405:

405 = 3⁴ x 5

Define k:

Let k be the number that when multiplied by 405 will give a perfect square.

Find k:

*Note: For a number to be a perfect square, the exponents have to be in multiple of 2s

405 = 3⁴ x 5

405k =  3⁴ x 5²

Therefore k = 5

Answer: The smallest natural number that 405 must multiplied to make it into a perfect square is 5.