Solve sqrt{45a}*sqrt{2}=15sqrt[6]{8}

$$\sqrt { 45 a } \cdot \sqrt { 2 } = 15 \sqrt[ 6 ] { 8 }$$

Solve for a

$$a=5$$

Steps for Solving Radical Equations

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}\sqrt{45a}}{\sqrt{2}}=\frac{15\sqrt{2}}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$\sqrt{45a}=\frac{15\sqrt{2}}{\sqrt{2}}$$

Divide 15\sqrt{2} by \sqrt{2}.

$$\sqrt{45a}=15$$

Square both sides of the equation.

$$45a=225$$

Divide both sides by 45.

$$\frac{45a}{45}=\frac{225}{45}$$

Dividing by 45 undoes the multiplication by 45.

$$a=\frac{225}{45}$$

Divide 225 by 45.

$$a=5$$