Basic Math Examples

$72 = \sqrt{3 h \div 2}$

Step 1

Rewrite the equation as $\sqrt{3 h \div 2} = 72$ .

$\sqrt{3 h \div 2} = 72$

Step 2

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

${\sqrt{3 h \div 2}}^{2} = 72^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 h \div 2}$ as ${(3 h \div 2)}^{\frac{1}{2}}$ .

${({(3 h \div 2)}^{\frac{1}{2}})}^{2} = 72^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({(3 h \div 2)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in ${({(3 h \div 2)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1.1

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

${(3 h \div 2)}^{\frac{1}{2} \cdot 2} = 72^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${(3 h \div 2)}^{\frac{1}{2} \cdot 2} = 72^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(3 h \div 2)}^{1} = 72^{2}$

Step 3.2.1.2

Rewrite the division as a fraction.

${(\frac{3 h}{2})}^{1} = 72^{2}$

Step 3.2.1.3

Simplify.

$\frac{3 h}{2} = 72^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Raise $72$ to the power of $2$ .

$\frac{3 h}{2} = 5184$

Step 4

Solve for $h$ .

Tap for more steps...

Step 4.1

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 h}{2} = \frac{2}{3} \cdot 5184$

Step 4.2

Simplify both sides of the equation.

Tap for more steps...

Step 4.2.1

Simplify the left side.

Tap for more steps...

Step 4.2.1.1

Simplify $\frac{2}{3} \cdot \frac{3 h}{2}$ .

Tap for more steps...

Step 4.2.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 h}{2} = \frac{2}{3} \cdot 5184$

Step 4.2.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 h) = \frac{2}{3} \cdot 5184$

Step 4.2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1.2.1

Factor $3$ out of $3 h$ .

$\frac{1}{3} (3 (h)) = \frac{2}{3} \cdot 5184$

Step 4.2.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 h) = \frac{2}{3} \cdot 5184$

Step 4.2.1.1.2.3

Rewrite the expression.

$h = \frac{2}{3} \cdot 5184$

Step 4.2.2

Simplify the right side.

Tap for more steps...

Step 4.2.2.1

Simplify $\frac{2}{3} \cdot 5184$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.2.1.1.1

Factor $3$ out of $5184$ .

$h = \frac{2}{3} \cdot (3 (1728))$

Step 4.2.2.1.1.2

Cancel the common factor.

$h = \frac{2}{3} \cdot (3 \cdot 1728)$

Step 4.2.2.1.1.3

Rewrite the expression.

$h = 2 \cdot 1728$

Step 4.2.2.1.2

Multiply $2$ by $1728$ .

$h = 3456$