Question

if the square root of 32 is irrational, what is the smallest number we can multiply it by to get a rational product?

Answer 1

Answer: Correct answer is
`√(2)`

Explanation:

Irrational number is one which cannot be written in the form of p/q.The square root of 32 is an irrational number, which means if we convert it into a decimal point, it would continue and will not stop.It means it will be non-terminating and non repeating decimals.The square root of 32 will not end and it's will have non repeating digits also.

`√(32)` is
`√(16)`*
`√(2)` .

⇒
`√(16)` = 4

⇒ so
`√(32)` = 4*
`√(2)`

now square root of 32 comes out to be 4*
`√(2)`

we will multiply it with
`√(2)` to get a rational product

i.e 4*
`√(2)` *
`√(2)` (
`√(2)`*
`√(2)` = 2 )

⇒ 4*2

⇒ 8

we obtain 8 as a rational number. so
`√(2)` is the smallest number with which we will multiply square root of 32 to get a rational product.