Question

is it rational or irrational please proove
$5 \sqrt{32}$

Answer 1

hope it help u a lot

Answer 2

Let us assume 5√32 be a rational no....
then it can be expressed in pq form

i.e. p/q = 5 × 4√2. ( √32 = 4√2)
p/20q = √2

we know that p/q is rational also 1/20 is rational
that is why √2 is rational no.
but it contradicts the fact that √2 is irrational

This contradiction has been arisen by assuming 5√32 a rational no

So 5√32 is irrational...

Hope it will be helpful..