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

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

Evaluate

$$6\sqrt{3}\left(\sqrt{15}-5\right)\approx -11.712300632$$

Solution Steps

Use the distributive property to multiply 3\sqrt{15} by 2\sqrt{3}-2\sqrt{5}.

$$6\sqrt{3}\sqrt{15}-6\sqrt{15}\sqrt{5}$$

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

$$6\sqrt{3}\sqrt{3}\sqrt{5}-6\sqrt{15}\sqrt{5}$$

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

$$6\times 3\sqrt{5}-6\sqrt{15}\sqrt{5}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{5}-6\sqrt{15}\sqrt{5}$$

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}.

$$18\sqrt{5}-6\sqrt{5}\sqrt{3}\sqrt{5}$$

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

$$18\sqrt{5}-6\times 5\sqrt{3}$$

Multiply -6 and 5 to get -30.

$$18\sqrt{5}-30\sqrt{3}$$

Factor

$$6 \sqrt{3} {(\sqrt{3} \sqrt{5} - 5)} = -11.712300632$$