Solve for l 4=2 square root of l/3.3

$4 = 2 \sqrt{\frac{l}{3.3}}$

Rewrite the equation as $2 \sqrt{\frac{l}{3.3}} = 4$ .

$2 \sqrt{\frac{l}{3.3}} = 4$

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

${(2 \sqrt{\frac{l}{3.3}})}^{2} = 4^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{3.3}}$ as ${(\frac{l}{3.3})}^{\frac{1}{2}}$ .

${(2 {(\frac{l}{3.3})}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${(2 {(\frac{l}{3.3})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(2 {(\frac{1 l}{3.3})}^{\frac{1}{2}})}^{2} = 4^{2}$

Factor $3.3$ out of $3.3$ .

${(2 {(\frac{1 l}{3.3 (1)})}^{\frac{1}{2}})}^{2} = 4^{2}$

Separate fractions.

${(2 {(\frac{1}{3.3} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the expression.

Divide $1$ by $3.3$ .

${(2 {(0.\overline{30} \frac{l}{1})}^{\frac{1}{2}})}^{2} = 4^{2}$

Divide $l$ by $1$ .

${(2 {(0.\overline{30} l)}^{\frac{1}{2}})}^{2} = 4^{2}$

Apply the product rule to $0.\overline{30} l$ .

${(2 ({0.\overline{30}}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = 4^{2}$

Rewrite $0.\overline{30}$ as ${0.55048188}^{2}$ .

${(2 ({({0.55048188}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = 4^{2}$

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

${(2 ({0.55048188}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 ({0.55048188}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = 4^{2}$

Rewrite the expression.

${(2 ({0.55048188}^{1} l^{\frac{1}{2}}))}^{2} = 4^{2}$

Evaluate the exponent.

${(2 (0.55048188 l^{\frac{1}{2}}))}^{2} = 4^{2}$

Multiply $0.55048188$ by $2$ .

${(1.10096376 l^{\frac{1}{2}})}^{2} = 4^{2}$

Apply the product rule to $1.10096376 l^{\frac{1}{2}}$ .

${1.10096376}^{2} {(l^{\frac{1}{2}})}^{2} = 4^{2}$

Raise $1.10096376$ to the power of $2$ .

$1.\overline{21} {(l^{\frac{1}{2}})}^{2} = 4^{2}$

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

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

$1.\overline{21} l^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$1.\overline{21} l^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

$1.\overline{21} l^{1} = 4^{2}$

Simplify.

$1.\overline{21} l = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$1.\overline{21} l = 16$

Divide each term in $1.\overline{21} l = 16$ by $1.\overline{21}$ and simplify.

Divide each term in $1.\overline{21} l = 16$ by $1.\overline{21}$ .

$\frac{1.\overline{21} l}{1.\overline{21}} = \frac{16}{1.\overline{21}}$

Simplify the left side.

Cancel the common factor of $1.\overline{21}$ .

Cancel the common factor.

$\frac{1.\overline{21} l}{1.\overline{21}} = \frac{16}{1.\overline{21}}$

Divide $l$ by $1$ .

$l = \frac{16}{1.\overline{21}}$

Simplify the right side.

Divide $16$ by $1.\overline{21}$ .

$l = 13.2$

Solve for l 4=2 square root of l/3.3

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