Solve (sqrt{15}-2sqrt{3})*(sqrt{5}+2)

$$( \sqrt { 15 } - 2 \sqrt { 3 } ) \times ( \sqrt { 5 } + 2 )$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{15}-2\sqrt{3} by each term of \sqrt{5}+2.

$$\sqrt{15}\sqrt{5}+2\sqrt{15}-2\sqrt{3}\sqrt{5}-4\sqrt{3}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\sqrt{5}\sqrt{3}\sqrt{5}+2\sqrt{15}-2\sqrt{3}\sqrt{5}-4\sqrt{3}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$5\sqrt{3}+2\sqrt{15}-2\sqrt{3}\sqrt{5}-4\sqrt{3}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$5\sqrt{3}+2\sqrt{15}-2\sqrt{15}-4\sqrt{3}$$

Combine 2\sqrt{15} and -2\sqrt{15} to get 0.

$$5\sqrt{3}-4\sqrt{3}$$

Combine 5\sqrt{3} and -4\sqrt{3} to get \sqrt{3}.

$$\sqrt{3}$$