Solve for D 51.3 = square root of 30D0.875*1

$51.3 = \sqrt{30 \cdot D \cdot 0.875 \cdot 1}$

Step 1

Rewrite the equation as $\sqrt{30 \cdot D \cdot 0.875 \cdot 1} = 51.3$ .

$\sqrt{30 \cdot D \cdot 0.875 \cdot 1} = 51.3$

Step 2

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

${\sqrt{30 \cdot D \cdot 0.875 \cdot 1}}^{2} = {51.3}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{30 \cdot D \cdot 0.875 \cdot 1}$ as ${(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}}$ .

${({(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}})}^{2} = {51.3}^{2}$

Simplify the left side.

Simplify ${({(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2}})}^{2}$ .

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

${(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2} \cdot 2} = {51.3}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(30 \cdot D \cdot 0.875 \cdot 1)}^{\frac{1}{2} \cdot 2} = {51.3}^{2}$

Rewrite the expression.

${(30 \cdot D \cdot 0.875 \cdot 1)}^{1} = {51.3}^{2}$

Multiply $0.875$ by $30$ .

${(26.25 D \cdot 1)}^{1} = {51.3}^{2}$

Simplify.

Multiply $26.25$ by $1$ .

${(26.25 D)}^{1} = {51.3}^{2}$

Simplify.

$26.25 D = {51.3}^{2}$

Simplify the right side.

Raise $51.3$ to the power of $2$ .

$26.25 D = 2631.69$

Step 4

Divide each term in $26.25 D = 2631.69$ by $26.25$ and simplify.

Divide each term in $26.25 D = 2631.69$ by $26.25$ .

$\frac{26.25 D}{26.25} = \frac{2631.69}{26.25}$

Simplify the left side.

Cancel the common factor of $26.25$ .

Cancel the common factor.

$\frac{26.25 D}{26.25} = \frac{2631.69}{26.25}$

Divide $D$ by $1$ .

$D = \frac{2631.69}{26.25}$

Simplify the right side.

Divide $2631.69$ by $26.25$ .

$D = 100.25485714$

Solve for D 51.3 = square root of 30*D*0.875*1