How do you multiply sqrt (x) * (x)?

Jun 13, 2015

$\sqrt{x} \cdot x = \sqrt{{x}^{3}}$

Explanation:

Knowing that $\sqrt{x} = {x}^{\frac{1}{2}}$
and using the properties:
${x}^{a} \cdot {x}^{b} = {x}^{a + b}$
${\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}$
you have:

$\sqrt{x} \cdot x = {x}^{\frac{1}{2}} \cdot {x}^{1} = {x}^{\frac{1}{2} + 1} = {x}^{\frac{3}{2}} = {\left({x}^{3}\right)}^{\frac{1}{2}} = \sqrt{{x}^{3}}$