Solve (12^2+3^2):(5-2)+(sqrt{216}-3)*(4+1)=

$$( 12 ^ { 2 } + 3 ^ { 2 } ) : ( 5 - 2 ) + ( \sqrt { 216 } - 3 ) \cdot ( 4 + 1 ) =$$

Evaluate

$$30\sqrt{6}+36\approx 109.484692283$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{144+3^{2}}{5-2}+\left(\sqrt{216}-3\right)\left(4+1\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{144+9}{5-2}+\left(\sqrt{216}-3\right)\left(4+1\right)$$

Add 144 and 9 to get 153.

$$\frac{153}{5-2}+\left(\sqrt{216}-3\right)\left(4+1\right)$$

Subtract 2 from 5 to get 3.

$$\frac{153}{3}+\left(\sqrt{216}-3\right)\left(4+1\right)$$

Divide 153 by 3 to get 51.

$$51+\left(\sqrt{216}-3\right)\left(4+1\right)$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$51+\left(6\sqrt{6}-3\right)\left(4+1\right)$$

Add 4 and 1 to get 5.

$$51+\left(6\sqrt{6}-3\right)\times 5$$

Use the distributive property to multiply 6\sqrt{6}-3 by 5.

$$51+30\sqrt{6}-15$$

Subtract 15 from 51 to get 36.

$$36+30\sqrt{6}$$