Question

Multiply root 3 by cube root of 5

Answer 1

$\sqrt{3} * \sqrt[3]{5}$
=$3^{ \frac{1}{2} } * 5^{ \frac{1}{3} }$
Multiply 1/2 with 3/3 and 1/3 with 2/2
=$3^{ \frac{1}{2}* \frac{3}{3} } * 5^{ \frac{1}{3}* \frac{2}{2} }$
=$3^{ \frac{3}{6} } * 5^{ \frac{2}{6} }$
=$\sqrt[6]{ 3^{3} } * \sqrt[6]{ 5^{2} }$
=$\sqrt[6]{27} * \sqrt[6]{25}$
=$\sqrt[6]{27*25}$
=$\sqrt[6]{675}$

Answer 2

$\sqrt[3]{5} * \sqrt{3}$
⇒ $5^{ \frac{1}{3} } * 3^{ \frac{1}{2} }$
⇒ $5^{ \frac{2}{6} } * 3^{ \frac{3}{6} }$
⇒$(5^2)^{ \frac{1}{6} } * (3^3)^{ \frac{1}{6} }$
⇒$(25)^{ \frac{1}{6} } * (27)^{ \frac{1}{6} }$
⇒$(25* 27)^{ \frac{1}{6} }$
⇒$(675)^{ \frac{1}{6} }$
⇒$\sqrt[6]{675}$