Algebra Examples

$75 = \frac{0.025 + 1.25}{0.025} \sqrt{2 (9.8) (h)}$

Step 1

Rewrite the equation as $\frac{0.025 + 1.25}{0.025} \cdot \sqrt{2 (9.8) h} = 75$ .

$\frac{0.025 + 1.25}{0.025} \cdot \sqrt{2 (9.8) h} = 75$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Multiply $2$ by $9.8$ .

$\frac{0.025 + 1.25}{0.025} \cdot \sqrt{19.6 h} = 75$

Step 2.2

Add $0.025$ and $1.25$ .

$\frac{1.275}{0.025} \cdot \sqrt{19.6 h} = 75$

Step 2.3

Divide $1.275$ by $0.025$ .

$51 \cdot \sqrt{19.6 h} = 75$

Step 3

Divide each term in $51 \cdot \sqrt{19.6 h} = 75$ by $51$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $51 \cdot \sqrt{19.6 h} = 75$ by $51$ .

$\frac{51 \cdot \sqrt{19.6 h}}{51} = \frac{75}{51}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $51$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{51 \cdot \sqrt{19.6 h}}{51} = \frac{75}{51}$

Step 3.2.1.2

Divide $\sqrt{19.6 h}$ by $1$ .

$\sqrt{19.6 h} = \frac{75}{51}$

Step 3.2.2

Rewrite $19.6 h$ as ${({2.10408857}^{2})}^{2} h$ .

Tap for more steps...

Step 3.2.2.1

Rewrite $19.6$ as ${4.42718872}^{2}$ .

$\sqrt{{4.42718872}^{2} h} = \frac{75}{51}$

Step 3.2.2.2

Rewrite $4.42718872$ as ${2.10408857}^{2}$ .

$\sqrt{{({2.10408857}^{2})}^{2} h} = \frac{75}{51}$

Step 3.2.3

Pull terms out from under the radical.

${2.10408857}^{2} \sqrt{h} = \frac{75}{51}$

Step 3.2.4

Raise $2.10408857$ to the power of $2$ .

$4.42718872 \sqrt{h} = \frac{75}{51}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Cancel the common factor of $75$ and $51$ .

Tap for more steps...

Step 3.3.1.1

Factor $3$ out of $75$ .

$4.42718872 \sqrt{h} = \frac{3 (25)}{51}$

Step 3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.1.2.1

Factor $3$ out of $51$ .

$4.42718872 \sqrt{h} = \frac{3 \cdot 25}{3 \cdot 17}$

Step 3.3.1.2.2

Cancel the common factor.

$4.42718872 \sqrt{h} = \frac{3 \cdot 25}{3 \cdot 17}$

Step 3.3.1.2.3

Rewrite the expression.

$4.42718872 \sqrt{h} = \frac{25}{17}$

Step 4

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

${(4.42718872 \sqrt{h})}^{2} = {(\frac{25}{17})}^{2}$

Step 5

Simplify each side of the equation.

Tap for more steps...

Step 5.1

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

${(4.42718872 h^{\frac{1}{2}})}^{2} = {(\frac{25}{17})}^{2}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Simplify ${(4.42718872 h^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 5.2.1.1

Apply the product rule to $4.42718872 h^{\frac{1}{2}}$ .

${4.42718872}^{2} {(h^{\frac{1}{2}})}^{2} = {(\frac{25}{17})}^{2}$

Step 5.2.1.2

Raise $4.42718872$ to the power of $2$ .

$19.6 {(h^{\frac{1}{2}})}^{2} = {(\frac{25}{17})}^{2}$

Step 5.2.1.3

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

Tap for more steps...

Step 5.2.1.3.1

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

$19.6 h^{\frac{1}{2} \cdot 2} = {(\frac{25}{17})}^{2}$

Step 5.2.1.3.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1.3.2.1

Cancel the common factor.

$19.6 h^{\frac{1}{2} \cdot 2} = {(\frac{25}{17})}^{2}$

Step 5.2.1.3.2.2

Rewrite the expression.

$19.6 h^{1} = {(\frac{25}{17})}^{2}$

Step 5.2.1.4

Simplify.

$19.6 h = {(\frac{25}{17})}^{2}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Simplify ${(\frac{25}{17})}^{2}$ .

Tap for more steps...

Step 5.3.1.1

Apply the product rule to $\frac{25}{17}$ .

$19.6 h = \frac{25^{2}}{17^{2}}$

Step 5.3.1.2

Raise $25$ to the power of $2$ .

$19.6 h = \frac{625}{17^{2}}$

Step 5.3.1.3

Raise $17$ to the power of $2$ .

$19.6 h = \frac{625}{289}$

Step 6

Divide each term in $19.6 h = \frac{625}{289}$ by $19.6$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $19.6 h = \frac{625}{289}$ by $19.6$ .

$\frac{19.6 h}{19.6} = \frac{\frac{625}{289}}{19.6}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $19.6$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{19.6 h}{19.6} = \frac{\frac{625}{289}}{19.6}$

Step 6.2.1.2

Divide $h$ by $1$ .

$h = \frac{\frac{625}{289}}{19.6}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$h = \frac{625}{289} \cdot \frac{1}{19.6}$

Step 6.3.2

Divide $1$ by $19.6$ .

$h = \frac{625}{289} \cdot 0.0510204$

Step 6.3.3

Multiply $\frac{625}{289} \cdot 0.0510204$ .

Tap for more steps...

Step 6.3.3.1

Combine $\frac{625}{289}$ and $0.0510204$ .

$h = \frac{625 \cdot 0.0510204}{289}$

Step 6.3.3.2

Multiply $625$ by $0.0510204$ .

$h = \frac{31.8877551}{289}$

Step 6.3.4

Divide $31.8877551$ by $289$ .

$h = 0.11033825$