Solve for T T=2pi square root of L/980

$T = 2 π \sqrt{\frac{L}{980}}$

Rewrite $\frac{L}{980}$ as ${(\frac{1}{14})}^{2} \frac{L}{5}$ .

Factor the perfect power $1^{2}$ out of $L$ .

$T = 2 π \sqrt{\frac{1^{2} L}{980}}$

Factor the perfect power $14^{2}$ out of $980$ .

$T = 2 π \sqrt{\frac{1^{2} L}{14^{2} \cdot 5}}$

Rearrange the fraction $\frac{1^{2} L}{14^{2} \cdot 5}$ .

$T = 2 π \sqrt{{(\frac{1}{14})}^{2} \frac{L}{5}}$

Pull terms out from under the radical.

$T = 2 π (\frac{1}{14} \sqrt{\frac{L}{5}})$

Rewrite $\sqrt{\frac{L}{5}}$ as $\frac{\sqrt{L}}{\sqrt{5}}$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L}}{\sqrt{5}})$

Multiply $\frac{\sqrt{L}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$T = 2 π (\frac{1}{14} (\frac{\sqrt{L}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}))$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{L}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{\sqrt{5} \sqrt{5}})$

Raise $\sqrt{5}$ to the power of $1$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}})$

Raise $\sqrt{5}$ to the power of $1$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{{\sqrt{5}}^{1 + 1}})$

Add $1$ and $1$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{{\sqrt{5}}^{2}})$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}})$

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

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}})$

Combine $\frac{1}{2}$ and $2$ .

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{5^{\frac{2}{2}}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{5^{\frac{2}{2}}})$

Rewrite the expression.

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{5^{1}})$

Evaluate the exponent.

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L} \sqrt{5}}{5})$

Combine using the product rule for radicals.

$T = 2 π (\frac{1}{14} \cdot \frac{\sqrt{L \cdot 5}}{5})$

Multiply $\frac{1}{14} \cdot \frac{\sqrt{L \cdot 5}}{5}$ .

Multiply $\frac{1}{14}$ by $\frac{\sqrt{L \cdot 5}}{5}$ .

$T = 2 π \frac{\sqrt{L \cdot 5}}{14 \cdot 5}$

Multiply $14$ by $5$ .

$T = 2 π \frac{\sqrt{L \cdot 5}}{70}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 π$ .

$T = 2 (π) \frac{\sqrt{L \cdot 5}}{70}$

Factor $2$ out of $70$ .

$T = 2 (π) \frac{\sqrt{L \cdot 5}}{2 (35)}$

Cancel the common factor.

$T = 2 π \frac{\sqrt{L \cdot 5}}{2 \cdot 35}$

Rewrite the expression.

$T = π \frac{\sqrt{L \cdot 5}}{35}$

Combine $π$ and $\frac{\sqrt{L \cdot 5}}{35}$ .

$T = \frac{π \sqrt{L \cdot 5}}{35}$

Move $5$ to the left of $L$ .

$T = \frac{π \sqrt{5 L}}{35}$

Solve for T T=2pi square root of L/980

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