Solve for l t=4 square root of l/5.3

$t = 4 \sqrt{\frac{l}{5.3}}$

Rewrite the equation as $4 \sqrt{\frac{l}{5.3}} = t$ .

$4 \sqrt{\frac{l}{5.3}} = t$

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

${(4 \sqrt{\frac{l}{5.3}})}^{2} = t^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{5.3}}$ as ${(\frac{l}{5.3})}^{\frac{1}{2}}$ .

${(4 {(\frac{l}{5.3})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the left side.

Simplify ${(4 {(\frac{l}{5.3})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(4 {(\frac{1 l}{5.3})}^{\frac{1}{2}})}^{2} = t^{2}$

Factor $5.3$ out of $5.3$ .

${(4 {(\frac{1 l}{5.3 (1)})}^{\frac{1}{2}})}^{2} = t^{2}$

Separate fractions.

${(4 {(\frac{1}{5.3} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = t^{2}$

Simplify the expression.

Divide $1$ by $5.3$ .

${(4 {(0.18867924 \frac{l}{1})}^{\frac{1}{2}})}^{2} = t^{2}$

Divide $l$ by $1$ .

${(4 {(0.18867924 l)}^{\frac{1}{2}})}^{2} = t^{2}$

Apply the product rule to $0.18867924 l$ .

${(4 ({0.18867924}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = t^{2}$

Rewrite $0.18867924$ as ${0.43437224}^{2}$ .

${(4 ({({0.43437224}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = t^{2}$

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

${(4 ({0.43437224}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 ({0.43437224}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = t^{2}$

Rewrite the expression.

${(4 ({0.43437224}^{1} l^{\frac{1}{2}}))}^{2} = t^{2}$

Evaluate the exponent.

${(4 (0.43437224 l^{\frac{1}{2}}))}^{2} = t^{2}$

Multiply $0.43437224$ by $4$ .

${(1.73748897 l^{\frac{1}{2}})}^{2} = t^{2}$

Apply the product rule to $1.73748897 l^{\frac{1}{2}}$ .

${1.73748897}^{2} {(l^{\frac{1}{2}})}^{2} = t^{2}$

Raise $1.73748897$ to the power of $2$ .

$3.01886792 {(l^{\frac{1}{2}})}^{2} = t^{2}$

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

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

$3.01886792 l^{\frac{1}{2} \cdot 2} = t^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3.01886792 l^{\frac{1}{2} \cdot 2} = t^{2}$

Rewrite the expression.

$3.01886792 l^{1} = t^{2}$

Simplify.

$3.01886792 l = t^{2}$

Divide each term in $3.01886792 l = t^{2}$ by $3.01886792$ and simplify.

Divide each term in $3.01886792 l = t^{2}$ by $3.01886792$ .

$\frac{3.01886792 l}{3.01886792} = \frac{t^{2}}{3.01886792}$

Simplify the left side.

Cancel the common factor of $3.01886792$ .

Cancel the common factor.

$\frac{3.01886792 l}{3.01886792} = \frac{t^{2}}{3.01886792}$

Divide $l$ by $1$ .

$l = \frac{t^{2}}{3.01886792}$

Simplify the right side.

Multiply by $1$ .

$l = \frac{1 t^{2}}{3.01886792}$

Factor $3.01886792$ out of $3.01886792$ .

$l = \frac{1 t^{2}}{3.01886792 (1)}$

Separate fractions.

$l = \frac{1}{3.01886792} \cdot \frac{t^{2}}{1}$

Divide $1$ by $3.01886792$ .

$l = 0.33125 \frac{t^{2}}{1}$

Divide $t^{2}$ by $1$ .

$l = 0.33125 t^{2}$

Solve for l t=4 square root of l/5.3

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