Solve for l 6.7=pi square root of (9.8l)/1.6

$6.7 = π \sqrt{\frac{9.8 l}{1.6}}$

Step 1

Rewrite the equation as $π \sqrt{\frac{9.8 l}{1.6}} = 6.7$ .

$π \sqrt{\frac{9.8 l}{1.6}} = 6.7$

Step 2

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

${(π \sqrt{\frac{9.8 l}{1.6}})}^{2} = {6.7}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{9.8 l}{1.6}}$ as ${(\frac{9.8 l}{1.6})}^{\frac{1}{2}}$ .

${(π {(\frac{9.8 l}{1.6})}^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Simplify the left side.

Simplify ${(π {(\frac{9.8 l}{1.6})}^{\frac{1}{2}})}^{2}$ .

Factor $9.8$ out of $9.8 l$ .

${(π {(\frac{9.8 (l)}{1.6})}^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Factor $1.6$ out of $1.6$ .

${(π {(\frac{9.8 (l)}{1.6 (1)})}^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Separate fractions.

${(π {(\frac{9.8}{1.6} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Simplify the expression.

Divide $9.8$ by $1.6$ .

${(π {(6.125 \frac{l}{1})}^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Divide $l$ by $1$ .

${(π {(6.125 l)}^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Apply the product rule to $6.125 l$ .

${(π ({6.125}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {6.7}^{2}$

Rewrite $6.125$ as ${2.47487373}^{2}$ .

${(π ({({2.47487373}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {6.7}^{2}$

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

${(π ({2.47487373}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {6.7}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(π ({2.47487373}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {6.7}^{2}$

Rewrite the expression.

${(π ({2.47487373}^{1} l^{\frac{1}{2}}))}^{2} = {6.7}^{2}$

Evaluate the exponent.

${(π (2.47487373 l^{\frac{1}{2}}))}^{2} = {6.7}^{2}$

Multiply $2.47487373$ by $π$ .

${(7.77504514 l^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Simplify the expression.

Apply the product rule to $7.77504514 l^{\frac{1}{2}}$ .

${7.77504514}^{2} {(l^{\frac{1}{2}})}^{2} = {6.7}^{2}$

Raise $7.77504514$ to the power of $2$ .

$60.45132695 {(l^{\frac{1}{2}})}^{2} = {6.7}^{2}$

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

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

$60.45132695 l^{\frac{1}{2} \cdot 2} = {6.7}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$60.45132695 l^{\frac{1}{2} \cdot 2} = {6.7}^{2}$

Rewrite the expression.

$60.45132695 l^{1} = {6.7}^{2}$

Simplify.

$60.45132695 l = {6.7}^{2}$

Simplify the right side.

Raise $6.7$ to the power of $2$ .

$60.45132695 l = 44.89$

Step 4

Divide each term in $60.45132695 l = 44.89$ by $60.45132695$ and simplify.

Divide each term in $60.45132695 l = 44.89$ by $60.45132695$ .

$\frac{60.45132695 l}{60.45132695} = \frac{44.89}{60.45132695}$

Simplify the left side.

Cancel the common factor of $60.45132695$ .

Cancel the common factor.

$\frac{60.45132695 l}{60.45132695} = \frac{44.89}{60.45132695}$

Divide $l$ by $1$ .

$l = \frac{44.89}{60.45132695}$

Simplify the right side.

Divide $44.89$ by $60.45132695$ .

$l = 0.74258088$

Solve for l 6.7=pi square root of (9.8l)/1.6

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