Solve for w square root of w=7

$\sqrt{w} = 7$

Step 1

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

${\sqrt{w}}^{2} = 7^{2}$

Step 2

Simplify each side of the equation.

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

${(w^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

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

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

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

$w^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$w^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

$w^{1} = 7^{2}$

Simplify.

$w = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$w = 49$