Solve for m square root of m=11

$\sqrt{m} = 11$

Step 1

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

${\sqrt{m}}^{2} = 11^{2}$

Step 2

Simplify each side of the equation.

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

${(m^{\frac{1}{2}})}^{2} = 11^{2}$

Simplify the left side.

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

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

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

$m^{\frac{1}{2} \cdot 2} = 11^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$m^{\frac{1}{2} \cdot 2} = 11^{2}$

Rewrite the expression.

$m^{1} = 11^{2}$

Simplify.

$m = 11^{2}$

Simplify the right side.

Raise $11$ to the power of $2$ .

$m = 121$