Answer: Correct answer is [tex]\sqrt{2}[/tex]
Step-by-step 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.
[tex]\sqrt{32}[/tex] is [tex]\sqrt{16}[/tex]*[tex]\sqrt{2}[/tex] .
⇒ [tex]\sqrt{16}[/tex] = 4
⇒ so [tex]\sqrt{32}[/tex] = 4*[tex]\sqrt{2}[/tex]
now square root of 32 comes out to be 4*[tex]\sqrt{2}[/tex]
we will multiply it with [tex]\sqrt{2}[/tex] to get a rational product
i.e 4*[tex]\sqrt{2}[/tex] * [tex]\sqrt{2}[/tex] ([tex]\sqrt{2}[/tex]*[tex]\sqrt{2}[/tex] = 2 )
⇒ 4*2
⇒ 8
we obtain 8 as a rational number. so [tex]\sqrt{2}[/tex] is the smallest number with which we will multiply square root of 32 to get a rational product.
