Solve (2-sqrt{5})quad(9)2sqrt{6}*3sqrt{3}*(-1/2sqrt{2})

$$( 2 - \sqrt { 5 } ) \quad ( 9 ) 2 \sqrt { 6 } \times 3 \sqrt { 3 } \times ( - \frac { 1 } { 2 } \sqrt { 2 } )$$

Evaluate

$$162\left(\sqrt{5}-2\right)\approx 38.243012355$$

Solution Steps

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$2\times 3\left(2-\sqrt{5}\right)\times 9\sqrt{3}\sqrt{2}\sqrt{3}\left(-\frac{1}{2}\right)\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$2\times 3\left(2-\sqrt{5}\right)\times 9\times 3\sqrt{2}\left(-\frac{1}{2}\right)\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\times 3\left(2-\sqrt{5}\right)\times 9\times 3\times 2\left(-\frac{1}{2}\right)$$

Multiply 2 and 3 to get 6.

$$6\left(2-\sqrt{5}\right)\times 9\times 3\times 2\left(-\frac{1}{2}\right)$$

Multiply 6 and 9 to get 54.

$$54\left(2-\sqrt{5}\right)\times 3\times 2\left(-\frac{1}{2}\right)$$

Multiply 54 and 3 to get 162.

$$162\left(2-\sqrt{5}\right)\times 2\left(-\frac{1}{2}\right)$$

Multiply 162 and 2 to get 324.

$$324\left(2-\sqrt{5}\right)\left(-\frac{1}{2}\right)$$

Express 324\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{324\left(-1\right)}{2}\left(2-\sqrt{5}\right)$$

Multiply 324 and -1 to get -324.

$$\frac{-324}{2}\left(2-\sqrt{5}\right)$$

Divide -324 by 2 to get -162.

$$-162\left(2-\sqrt{5}\right)$$

Use the distributive property to multiply -162 by 2-\sqrt{5}.

$$-324+162\sqrt{5}$$