Solve (4sqrt{3})(2sqrt{6}-5sqrt{15})

$$( 4 \sqrt { 3 } ) ( 2 \sqrt { 6 } - 5 \sqrt { 15 } )$$

Evaluate

$$12\left(2\sqrt{2}-5\sqrt{5}\right)\approx -100.222953153$$

Solution Steps

Use the distributive property to multiply 4\sqrt{3} by 2\sqrt{6}-5\sqrt{15}.

$$8\sqrt{3}\sqrt{6}-20\sqrt{3}\sqrt{15}$$

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}.

$$8\sqrt{3}\sqrt{3}\sqrt{2}-20\sqrt{3}\sqrt{15}$$

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

$$8\times 3\sqrt{2}-20\sqrt{3}\sqrt{15}$$

Multiply 8 and 3 to get 24.

$$24\sqrt{2}-20\sqrt{3}\sqrt{15}$$

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}.

$$24\sqrt{2}-20\sqrt{3}\sqrt{3}\sqrt{5}$$

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

$$24\sqrt{2}-20\times 3\sqrt{5}$$

Multiply -20 and 3 to get -60.

$$24\sqrt{2}-60\sqrt{5}$$