Solve for L T=2pi square root of L/K

$T = 2 π \sqrt{\frac{L}{K}}$

Step 1

Rewrite the equation as $2 π \sqrt{\frac{L}{K}} = T$ .

$2 π \sqrt{\frac{L}{K}} = T$

Step 2

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

${(2 π \sqrt{\frac{L}{K}})}^{2} = T^{2}$

Step 3

Simplify each side of the equation.

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

${(2 π {(\frac{L}{K})}^{\frac{1}{2}})}^{2} = T^{2}$

Simplify the left side.

Simplify ${(2 π {(\frac{L}{K})}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $\frac{L}{K}$ .

${(2 π \frac{L^{\frac{1}{2}}}{K^{\frac{1}{2}}})}^{2} = T^{2}$

Multiply $2 π \frac{L^{\frac{1}{2}}}{K^{\frac{1}{2}}}$ .

Combine $\frac{L^{\frac{1}{2}}}{K^{\frac{1}{2}}}$ and $2$ .

${(\frac{L^{\frac{1}{2}} \cdot 2}{K^{\frac{1}{2}}} π)}^{2} = T^{2}$

Combine $\frac{L^{\frac{1}{2}} \cdot 2}{K^{\frac{1}{2}}}$ and $π$ .

${(\frac{L^{\frac{1}{2}} \cdot 2 π}{K^{\frac{1}{2}}})}^{2} = T^{2}$

Move $2$ to the left of $L^{\frac{1}{2}}$ .

${(\frac{2 \cdot L^{\frac{1}{2}} π}{K^{\frac{1}{2}}})}^{2} = T^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 L^{\frac{1}{2}} π}{K^{\frac{1}{2}}}$ .

$\frac{{(2 L^{\frac{1}{2}} π)}^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

Apply the product rule to $2 L^{\frac{1}{2}} π$ .

$\frac{{(2 L^{\frac{1}{2}})}^{2} π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

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

$\frac{2^{2} {(L^{\frac{1}{2}})}^{2} π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

Simplify the numerator.

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

$\frac{4 {(L^{\frac{1}{2}})}^{2} π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

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

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

$\frac{4 L^{\frac{1}{2} \cdot 2} π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 L^{\frac{1}{2} \cdot 2} π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

Rewrite the expression.

$\frac{4 L^{1} π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

Simplify.

$\frac{4 L π^{2}}{{(K^{\frac{1}{2}})}^{2}} = T^{2}$

Simplify the denominator.

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

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

$\frac{4 L π^{2}}{K^{\frac{1}{2} \cdot 2}} = T^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 L π^{2}}{K^{\frac{1}{2} \cdot 2}} = T^{2}$

Rewrite the expression.

$\frac{4 L π^{2}}{K^{1}} = T^{2}$

Simplify.

$\frac{4 L π^{2}}{K} = T^{2}$

Step 4

Solve for $L$ .

Multiply both sides by $K$ .

$\frac{4 L π^{2}}{K} K = T^{2} K$

Simplify the left side.

Cancel the common factor of $K$ .

Cancel the common factor.

$\frac{4 L π^{2}}{K} K = T^{2} K$

Rewrite the expression.

$4 L π^{2} = T^{2} K$

Divide each term in $4 L π^{2} = T^{2} K$ by $4 π^{2}$ and simplify.

Divide each term in $4 L π^{2} = T^{2} K$ by $4 π^{2}$ .

$\frac{4 L π^{2}}{4 π^{2}} = \frac{T^{2} K}{4 π^{2}}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 L π^{2}}{4 π^{2}} = \frac{T^{2} K}{4 π^{2}}$

Rewrite the expression.

$\frac{L π^{2}}{π^{2}} = \frac{T^{2} K}{4 π^{2}}$

Cancel the common factor of $π^{2}$ .

Cancel the common factor.

$\frac{L π^{2}}{π^{2}} = \frac{T^{2} K}{4 π^{2}}$

Divide $L$ by $1$ .

$L = \frac{T^{2} K}{4 π^{2}}$

Solve for L T=2pi square root of L/K

Related Questions

Support LCMGCF.com by disabling your adblocker.