Solve 3sqrt{12}5(2+3)+90*3(13-3)div2

$$3 \sqrt { 12 } 5 ( 2 + 3 ) + 90 \times 3 ( 13 - 3 ) \div 2$$

Evaluate

$$150\left(\sqrt{3}+9\right)\approx 1609.807621135$$

Solution Steps

Multiply 3 and 5 to get 15.

$$15\sqrt{12}\left(2+3\right)+\frac{90\times 3\left(13-3\right)}{2}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$15\times 2\sqrt{3}\left(2+3\right)+\frac{90\times 3\left(13-3\right)}{2}$$

Multiply 15 and 2 to get 30.

$$30\sqrt{3}\left(2+3\right)+\frac{90\times 3\left(13-3\right)}{2}$$

Add 2 and 3 to get 5.

$$30\sqrt{3}\times 5+\frac{90\times 3\left(13-3\right)}{2}$$

Multiply 30 and 5 to get 150.

$$150\sqrt{3}+\frac{90\times 3\left(13-3\right)}{2}$$

Multiply 90 and 3 to get 270.

$$150\sqrt{3}+\frac{270\left(13-3\right)}{2}$$

Subtract 3 from 13 to get 10.

$$150\sqrt{3}+\frac{270\times 10}{2}$$

Multiply 270 and 10 to get 2700.

$$150\sqrt{3}+\frac{2700}{2}$$

Divide 2700 by 2 to get 1350.

$$150\sqrt{3}+1350$$

Factor

$$150 {(\sqrt{3} + 9)} = 1609.807621135$$