Question

What is the square root of m6?

Answer 1

Answer:

$\sf\large\boxed{\text{if}\ m\geq0,\ \text{then}\ \sf\sqrt{m^6}=m^3}\\\\\sf\boxed{\text{if}\sf\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3}$

Step-by-step explanation:

$\sf\sqrt{m^6}=\sf\sqrt{m^{3\cdot2}}\sf\qquad\text{use}\ \sf\:(a^n)^m=a^{nm}\\\\=\sf\sqrt{(m^3)^2}\qquad\text{use}\ \sf\sqrt{a^2}=|a|\\\\=\sf\:|m^3|\\\\ \sf\text{if}\ m\geq0,\ \text{then}\ \sqrt{m^6}=m^3\\\\\sf\text{if}\ m<0,\ \text{then}\ \sqrt{m^6}=-m^3$

Answer 2

$\rule{300}{1.05}$

Answer:

$\sqrt{m^6}:\quad m^3$

Step-by-step explanation:

$\rule{300}{1.05}$

$\sqrt{m^6}$

$\rule{300}{1.05}$

$\sqrt{a}=a^{\dfrac{1}{2}}$

$=\left(m^6\right)^{\dfrac{1}{2}}$

$\rule{300}{1.05}$

$\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0$

$=m^{6\cdot \dfrac{1}{2}}$

$\rule{300}{1.05}$

$6\cdot \dfrac{1}{2}$

$\rule{300}{0.5}$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:6=\dfrac{6}{1}$

$=\dfrac{6}{1}\cdot \dfrac{1}{2}$

$\rule{300}{0.5}$

$\mathrm{Cross-cancel\:common\:factor:}\:2$

$=\dfrac{3}{1}$

$\rule{300}{0.5}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{a}{1}=a$

$=3$

$\rule{300}{1.05}$

$=m^3$

$\rule{300}{1.05}$