Algebra Examples

$0.81 = 0.5 \sqrt{h}$

Step 1

Rewrite the equation as $0.5 \sqrt{h} = 0.81$ .

$0.5 \sqrt{h} = 0.81$

Step 2

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

${(0.5 \sqrt{h})}^{2} = {0.81}^{2}$

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 $\sqrt{h}$ as $h^{\frac{1}{2}}$ .

${(0.5 h^{\frac{1}{2}})}^{2} = {0.81}^{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${(0.5 h^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 3.2.1.1

Apply the product rule to $0.5 h^{\frac{1}{2}}$ .

${0.5}^{2} {(h^{\frac{1}{2}})}^{2} = {0.81}^{2}$

Step 3.2.1.2

Raise $0.5$ to the power of $2$ .

$0.25 {(h^{\frac{1}{2}})}^{2} = {0.81}^{2}$

Step 3.2.1.3

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

Tap for more steps...

Step 3.2.1.3.1

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

$0.25 h^{\frac{1}{2} \cdot 2} = {0.81}^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.3.2.1

Cancel the common factor.

$0.25 h^{\frac{1}{2} \cdot 2} = {0.81}^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$0.25 h^{1} = {0.81}^{2}$

Step 3.2.1.4

Simplify.

$0.25 h = {0.81}^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Raise $0.81$ to the power of $2$ .

$0.25 h = 0.6561$

Step 4

Divide each term in $0.25 h = 0.6561$ by $0.25$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $0.25 h = 0.6561$ by $0.25$ .

$\frac{0.25 h}{0.25} = \frac{0.6561}{0.25}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $0.25$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{0.25 h}{0.25} = \frac{0.6561}{0.25}$

Step 4.2.1.2

Divide $h$ by $1$ .

$h = \frac{0.6561}{0.25}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0.6561$ by $0.25$ .

$h = 2.6244$