Question

$( \sqrt{2m + \sqrt{3n) {?}^{2} } }$
$( \sqrt{2m + \sqrt{3n) {?}^{2} } }$
Using the standard formulae, expand each of the following ​

Answer 1

Answer:

$\mathrm{Simplify}\:\left(\sqrt{2m+\sqrt{3n}}\right)^2:\quad 2m+\sqrt{3}\sqrt{n}$

Step-by-step explanation:

$\left(\sqrt{2m+\sqrt{3n}}\right)^2$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}=a^{\frac{1}{2}}$

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

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}$

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

$=2m+\sqrt{3n}$

$\mathrm{Apply\:radical\:rule:\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0$

$=2m+\sqrt{3}\sqrt{n}$