Solve for l 2.5=2 square root of l/3.5

$2.5 = 2 \sqrt{\frac{l}{3.5}}$

Step 1

Rewrite the equation as $2 \sqrt{\frac{l}{3.5}} = 2.5$ .

$2 \sqrt{\frac{l}{3.5}} = 2.5$

Step 2

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

${(2 \sqrt{\frac{l}{3.5}})}^{2} = {2.5}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{l}{3.5}}$ as ${(\frac{l}{3.5})}^{\frac{1}{2}}$ .

${(2 {(\frac{l}{3.5})}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Simplify the left side.

Simplify ${(2 {(\frac{l}{3.5})}^{\frac{1}{2}})}^{2}$ .

Multiply by $1$ .

${(2 {(\frac{1 l}{3.5})}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Factor $3.5$ out of $3.5$ .

${(2 {(\frac{1 l}{3.5 (1)})}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Separate fractions.

${(2 {(\frac{1}{3.5} \cdot \frac{l}{1})}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Simplify the expression.

Divide $1$ by $3.5$ .

${(2 {(0.\overline{285714} \frac{l}{1})}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Divide $l$ by $1$ .

${(2 {(0.\overline{285714} l)}^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Apply the product rule to $0.\overline{285714} l$ .

${(2 ({0.\overline{285714}}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {2.5}^{2}$

Rewrite $0.\overline{285714}$ as ${0.53452248}^{2}$ .

${(2 ({({0.53452248}^{2})}^{\frac{1}{2}} l^{\frac{1}{2}}))}^{2} = {2.5}^{2}$

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

${(2 ({0.53452248}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {2.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 ({0.53452248}^{2 (\frac{1}{2})} l^{\frac{1}{2}}))}^{2} = {2.5}^{2}$

Rewrite the expression.

${(2 ({0.53452248}^{1} l^{\frac{1}{2}}))}^{2} = {2.5}^{2}$

Evaluate the exponent.

${(2 (0.53452248 l^{\frac{1}{2}}))}^{2} = {2.5}^{2}$

Multiply $0.53452248$ by $2$ .

${(1.06904496 l^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Apply the product rule to $1.06904496 l^{\frac{1}{2}}$ .

${1.06904496}^{2} {(l^{\frac{1}{2}})}^{2} = {2.5}^{2}$

Raise $1.06904496$ to the power of $2$ .

$1.\overline{142857} {(l^{\frac{1}{2}})}^{2} = {2.5}^{2}$

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

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

$1.\overline{142857} l^{\frac{1}{2} \cdot 2} = {2.5}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$1.\overline{142857} l^{\frac{1}{2} \cdot 2} = {2.5}^{2}$

Rewrite the expression.

$1.\overline{142857} l^{1} = {2.5}^{2}$

Simplify.

$1.\overline{142857} l = {2.5}^{2}$

Simplify the right side.

Raise $2.5$ to the power of $2$ .

$1.\overline{142857} l = 6.25$

Step 4

Divide each term in $1.\overline{142857} l = 6.25$ by $1.\overline{142857}$ and simplify.

Divide each term in $1.\overline{142857} l = 6.25$ by $1.\overline{142857}$ .

$\frac{1.\overline{142857} l}{1.\overline{142857}} = \frac{6.25}{1.\overline{142857}}$

Simplify the left side.

Cancel the common factor of $1.\overline{142857}$ .

Cancel the common factor.

$\frac{1.\overline{142857} l}{1.\overline{142857}} = \frac{6.25}{1.\overline{142857}}$

Divide $l$ by $1$ .

$l = \frac{6.25}{1.\overline{142857}}$

Simplify the right side.

Divide $6.25$ by $1.\overline{142857}$ .

$l = 5.46875$

Solve for l 2.5=2 square root of l/3.5

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