Question

Using the laws of indices, simplify the following:-

√h × √h³ =

Answer 1

$\sqrt h\cdot\sqrt{h^3}=\\ h^{\frac{1}{2}}\cdot \left(h^3\right)^{\frac{1}{2}}=\\ h^{\frac{1}{2}}\cdot h^{\frac{3}{2}}=\\ h^{\frac{1}{2}+\frac{3}{2}}=\\ h^{\frac{4}{2}}=\\ h^2$

or other way

$\sqrt h\cdot\sqrt{h^3}=\\ \sqrt{h^4}=\\ \sqrt{(h^2)^2}=\\ |h^2|=\\ h^2$