Solve for k w = square root of k/m

$w = \sqrt{\frac{k}{m}}$

Step 1

Rewrite the equation as $\sqrt{\frac{k}{m}} = w$ .

$\sqrt{\frac{k}{m}} = w$

Step 2

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

${\sqrt{\frac{k}{m}}}^{2} = w^{2}$

Step 3

Simplify each side of the equation.

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

${({(\frac{k}{m})}^{\frac{1}{2}})}^{2} = w^{2}$

Simplify the left side.

Simplify ${({(\frac{k}{m})}^{\frac{1}{2}})}^{2}$ .

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

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

${(\frac{k}{m})}^{\frac{1}{2} \cdot 2} = w^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{k}{m})}^{\frac{1}{2} \cdot 2} = w^{2}$

Rewrite the expression.

${(\frac{k}{m})}^{1} = w^{2}$

Simplify.

$\frac{k}{m} = w^{2}$

Step 4

Solve for $k$ .

Multiply both sides by $m$ .

$\frac{k}{m} m = w^{2} m$

Simplify the left side.

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{k}{m} m = w^{2} m$

Rewrite the expression.

$k = w^{2} m$