Solve sqrt{20*45}-frac{sqrt{32}}{50}=

$$\sqrt { 20 \cdot 45 } - \frac { \sqrt { 32 } } { 50 } =$$

Evaluate

$$-\frac{2\sqrt{2}}{25}+30\approx 29.886862915$$

Solution Steps

Multiply 20 and 45 to get 900.

$$\sqrt{900}-\frac{\sqrt{32}}{50}$$

Calculate the square root of 900 and get 30.

$$30-\frac{\sqrt{32}}{50}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$30-\frac{4\sqrt{2}}{50}$$

Divide 4\sqrt{2} by 50 to get \frac{2}{25}\sqrt{2}.

$$30-\frac{2}{25}\sqrt{2}$$

Factor

$$\frac{2 {(375 - \sqrt{2})}}{25} = 29.886862915010152$$