Solve for m 3 square root of 16-m=15

$3 \sqrt{16 - m} = 15$

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

${(3 \sqrt{16 - m})}^{2} = 15^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{16 - m}$ as ${(16 - m)}^{\frac{1}{2}}$ .

${(3 {(16 - m)}^{\frac{1}{2}})}^{2} = 15^{2}$

Simplify the left side.

Simplify ${(3 {(16 - m)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $3 {(16 - m)}^{\frac{1}{2}}$ .

$3^{2} {({(16 - m)}^{\frac{1}{2}})}^{2} = 15^{2}$

Raise $3$ to the power of $2$ .

$9 {({(16 - m)}^{\frac{1}{2}})}^{2} = 15^{2}$

Multiply the exponents in ${({(16 - m)}^{\frac{1}{2}})}^{2}$ .

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

$9 {(16 - m)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 {(16 - m)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Rewrite the expression.

$9 {(16 - m)}^{1} = 15^{2}$

Simplify.

$9 (16 - m) = 15^{2}$

Apply the distributive property.

$9 \cdot 16 + 9 (- m) = 15^{2}$

Multiply.

Multiply $9$ by $16$ .

$144 + 9 (- m) = 15^{2}$

Multiply $- 1$ by $9$ .

$144 - 9 m = 15^{2}$

Simplify the right side.

Raise $15$ to the power of $2$ .

$144 - 9 m = 225$

Solve for $m$ .

Move all terms not containing $m$ to the right side of the equation.

Subtract $144$ from both sides of the equation.

$- 9 m = 225 - 144$

Subtract $144$ from $225$ .

$- 9 m = 81$

Divide each term in $- 9 m = 81$ by $- 9$ and simplify.

Divide each term in $- 9 m = 81$ by $- 9$ .

$\frac{- 9 m}{- 9} = \frac{81}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 m}{- 9} = \frac{81}{- 9}$

Divide $m$ by $1$ .

$m = \frac{81}{- 9}$

Simplify the right side.

Divide $81$ by $- 9$ .

$m = - 9$

Solve for m 3 square root of 16-m=15

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