Simplify square root of square root of square root of x^8

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

Step 1

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

$\sqrt{\sqrt{\sqrt{{(x^{4})}^{2}}}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{\sqrt{x^{4}}}$

Step 3

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

$\sqrt{\sqrt{{(x^{2})}^{2}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{x^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$x$