Question

Simplify this radical.
Square root of x to the 13th power

Answer 1

Answer:

x^6$\sqrt{x}$

Step-by-step explanation:

we have:

$\sqrt{x^{13}}$

we can write:

$\sqrt{x^{13}}$ :$\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}$

we know:

$\sqrt{x^{2}} = x$

so we have:

$\sqrt{x^{13}}$ =$\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}$

we have:

$\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}$=

$x^{6} \sqrt{x}$

Answer 2

Answer:

$\large\boxed{\sqrt{x^{13}}=x^6\sqrt{x}}$

Step-by-step explanation:

$\sqrt{x^{13}}=\sqrt{x^{12+1}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\sqrt{x^{12}x^1}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{x^{12}}\cdot\sqrt{x}=\sqrt{x^{6\cdot2}}\cdot\sqrt{x}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(x^6)^2}\cdot\sqrt{x}\qquad\text{use}\ \sqrt{x^2}=|x|\\\\=|x^6|\sqrt{x}=x^6\sqrt{x}\ \text{because}\ x^6\geq0$