Solve sqrt{5}-(sqrt{3}-3)*sqrt{3}-3*(3+sqrt{3})=

$$\sqrt { 5 } - ( \sqrt { 3 } - 3 ) \cdot \sqrt { 3 } - 3 \cdot ( 3 + \sqrt { 3 } ) =$$

Evaluate

$$\sqrt{5}-12\approx -9.763932023$$

Solution Steps

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

$$\sqrt{5}-\left(\left(\sqrt{3}\right)^{2}-3\sqrt{3}\right)-3\left(3+\sqrt{3}\right)$$

The square of \sqrt{3} is 3.

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

To find the opposite of 3-3\sqrt{3}, find the opposite of each term.

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

The opposite of -3\sqrt{3} is 3\sqrt{3}.

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

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

$$\sqrt{5}-3+3\sqrt{3}-9-3\sqrt{3}$$

Subtract 9 from -3 to get -12.

$$\sqrt{5}-12+3\sqrt{3}-3\sqrt{3}$$

Combine 3\sqrt{3} and -3\sqrt{3} to get 0.

$$\sqrt{5}-12$$