Algebra Examples

$\sqrt{x^{16} + 16 x^{8}}$

Step 1

Factor $x^{8}$ out of $x^{16} + 16 x^{8}$ .

Tap for more steps...

Step 1.1

Factor $x^{8}$ out of $x^{16}$ .

$\sqrt{x^{8} x^{8} + 16 x^{8}}$

Step 1.2

Factor $x^{8}$ out of $16 x^{8}$ .

$\sqrt{x^{8} x^{8} + x^{8} \cdot 16}$

Step 1.3

Factor $x^{8}$ out of $x^{8} x^{8} + x^{8} \cdot 16$ .

$\sqrt{x^{8} (x^{8} + 16)}$

Step 2

Rewrite $x^{8} (x^{8} + 16)$ as ${({(x^{2})}^{2})}^{2} (x^{8} + 16)$ .

Tap for more steps...

Step 2.1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\sqrt{{(x^{4})}^{2} (x^{8} + 16)}$

Step 2.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\sqrt{{({(x^{2})}^{2})}^{2} (x^{8} + 16)}$

Step 3

Pull terms out from under the radical.

${(x^{2})}^{2} \sqrt{x^{8} + 16}$

Step 4

Multiply the exponents in ${(x^{2})}^{2}$ .

Tap for more steps...

Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2 \cdot 2} \sqrt{x^{8} + 16}$

Step 4.2

Multiply $2$ by $2$ .

$x^{4} \sqrt{x^{8} + 16}$