Solve for b b = square root of 182.8* square root of 182.8

$b = \sqrt{182.8} \cdot \sqrt{182.8}$

Step 1

Multiply $\sqrt{182.8} \sqrt{182.8}$ .

Raise $\sqrt{182.8}$ to the power of $1$ .

$b = {\sqrt{182.8}}^{1} \sqrt{182.8}$

Raise $\sqrt{182.8}$ to the power of $1$ .

$b = {\sqrt{182.8}}^{1} {\sqrt{182.8}}^{1}$

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

$b = {\sqrt{182.8}}^{1 + 1}$

Add $1$ and $1$ .

$b = {\sqrt{182.8}}^{2}$

Step 2

Rewrite ${\sqrt{182.8}}^{2}$ as $182.8$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{182.8}$ as ${182.8}^{\frac{1}{2}}$ .

$b = {({182.8}^{\frac{1}{2}})}^{2}$

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

$b = {182.8}^{\frac{1}{2} \cdot 2}$

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

$b = {182.8}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$b = {182.8}^{\frac{2}{2}}$

Rewrite the expression.

$b = {182.8}^{1}$

Evaluate the exponent.

$b = 182.8$