Solve for y y^4=400

$y^{4} = 400$

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt[4]{400}$

Simplify $\pm \sqrt[4]{400}$ .

Rewrite $400$ as $2^{4} \cdot 25$ .

Factor $16$ out of $400$ .

$y = \pm \sqrt[4]{16 (25)}$

Rewrite $16$ as $2^{4}$ .

$y = \pm \sqrt[4]{2^{4} \cdot 25}$

Pull terms out from under the radical.

$y = \pm 2 \sqrt[4]{25}$

Rewrite $25$ as $5^{2}$ .

$y = \pm 2 \sqrt[4]{5^{2}}$

Rewrite $\sqrt[4]{5^{2}}$ as $\sqrt{\sqrt{5^{2}}}$ .

$y = \pm 2 \sqrt{\sqrt{5^{2}}}$

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

$y = \pm 2 \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = 2 \sqrt{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 2 \sqrt{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = 2 \sqrt{5}, - 2 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$y = 2 \sqrt{5}, - 2 \sqrt{5}$

Decimal Form:

$y = 4.47213595 \dots, - 4.47213595 \dots$