Solve for d 80 = square root of 64d

$80 = \sqrt{64 d}$

Rewrite the equation as $\sqrt{64 d} = 80$ .

$\sqrt{64 d} = 80$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{64 d}}^{2} = 80^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{64 d}$ as ${(64 d)}^{\frac{1}{2}}$ .

${({(64 d)}^{\frac{1}{2}})}^{2} = 80^{2}$

Simplify the left side.

Simplify ${({(64 d)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(64 d)}^{\frac{1}{2}})}^{2}$ .

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

${(64 d)}^{\frac{1}{2} \cdot 2} = 80^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(64 d)}^{\frac{1}{2} \cdot 2} = 80^{2}$

Rewrite the expression.

${(64 d)}^{1} = 80^{2}$

Simplify.

$64 d = 80^{2}$

Simplify the right side.

Raise $80$ to the power of $2$ .

$64 d = 6400$

Divide each term in $64 d = 6400$ by $64$ and simplify.

Divide each term in $64 d = 6400$ by $64$ .

$\frac{64 d}{64} = \frac{6400}{64}$

Simplify the left side.

Cancel the common factor of $64$ .

Cancel the common factor.

$\frac{64 d}{64} = \frac{6400}{64}$

Divide $d$ by $1$ .

$d = \frac{6400}{64}$

Simplify the right side.

Divide $6400$ by $64$ .

$d = 100$