Simplify square root of 324-(2-9)^2+162÷(3^3)

$\sqrt{324} - {(2 - 9)}^{2} + 162 \div 3^{3}$

Step 1

Find the common denominator.

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

$\sqrt{324} - {(2 - 9)}^{2} + 162 \div 27$

Write $\sqrt{324}$ as a fraction with denominator $1$ .

$\frac{\sqrt{324}}{1} - {(2 - 9)}^{2} + 162 \div 27$

Multiply $\frac{\sqrt{324}}{1}$ by $\frac{27}{27}$ .

$\frac{\sqrt{324}}{1} \cdot \frac{27}{27} - {(2 - 9)}^{2} + 162 \div 27$

Multiply $\frac{\sqrt{324}}{1}$ by $\frac{27}{27}$ .

$\frac{\sqrt{324} \cdot 27}{27} - {(2 - 9)}^{2} + 162 \div 27$

Write $- {(2 - 9)}^{2}$ as a fraction with denominator $1$ .

$\frac{\sqrt{324} \cdot 27}{27} + \frac{- {(2 - 9)}^{2}}{1} + 162 \div 27$

Multiply $\frac{- {(2 - 9)}^{2}}{1}$ by $\frac{27}{27}$ .

$\frac{\sqrt{324} \cdot 27}{27} + \frac{- {(2 - 9)}^{2}}{1} \cdot \frac{27}{27} + 162 \div 27$

Multiply $\frac{- {(2 - 9)}^{2}}{1}$ by $\frac{27}{27}$ .

$\frac{\sqrt{324} \cdot 27}{27} + \frac{- {(2 - 9)}^{2} \cdot 27}{27} + 162 \div 27$

Step 2

Combine the numerators over the common denominator.

$\frac{\sqrt{324} \cdot 27 - {(2 - 9)}^{2} \cdot 27 + 162}{27}$

Step 3

Simplify each term.

Rewrite $324$ as $18^{2}$ .

$\frac{\sqrt{18^{2}} \cdot 27 - {(2 - 9)}^{2} \cdot 27 + 162}{27}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{18 \cdot 27 - {(2 - 9)}^{2} \cdot 27 + 162}{27}$

Multiply $18$ by $27$ .

$\frac{486 - {(2 - 9)}^{2} \cdot 27 + 162}{27}$

Subtract $9$ from $2$ .

$\frac{486 - {(- 7)}^{2} \cdot 27 + 162}{27}$

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

$\frac{486 - 1 \cdot 49 \cdot 27 + 162}{27}$

Multiply $- 1 \cdot 49 \cdot 27$ .

Multiply $- 1$ by $49$ .

$\frac{486 - 49 \cdot 27 + 162}{27}$

Multiply $- 49$ by $27$ .

$\frac{486 - 1323 + 162}{27}$

Step 4

Simplify the expression.

Subtract $1323$ from $486$ .

$\frac{- 837 + 162}{27}$

Add $- 837$ and $162$ .

$\frac{- 675}{27}$

Divide $- 675$ by $27$ .

$- 25$