Question

Solve the equation $y^4-64=0$.

Short answer

The solution for the equation is $y=\pm i2\sqrt{2},y=\pm 2\sqrt{2}$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $y^4-64=0$.

Step 2. Simplify the equation.

The given equation $y^4-64=0$ is solved as:

$\begin{array}{c}{y}^4-64=\mathrm{0....}\left(\text{Given}\right)\\ \left(y^2+8\right)\left(y^2-8\right)=0\\ y^2+8=0\text{or}{y}^2-8=0\\ y^2=-8\text{or}{y}^2=8\\ y=\pm i2\sqrt{2}\text{or}y=\pm 2\sqrt{2}\end{array}$

Step 3. Conclusion.

The solution for the given equation is $y=\pm i2\sqrt{2},y=\pm 2\sqrt{2}$.