Solve sqrt{6}(9sqrt{2}-5sqrt{12})

$$\sqrt { 6 } ( 9 \sqrt { 2 } - 5 \sqrt { 12 } )$$

Evaluate

$$6\left(3\sqrt{3}-5\sqrt{2}\right)\approx -11.249492335$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply -5 and 2 to get -10.

$$\sqrt{6}\left(9\sqrt{2}-10\sqrt{3}\right)$$

Use the distributive property to multiply \sqrt{6} by 9\sqrt{2}-10\sqrt{3}.

$$9\sqrt{6}\sqrt{2}-10\sqrt{6}\sqrt{3}$$

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

$$9\sqrt{2}\sqrt{3}\sqrt{2}-10\sqrt{6}\sqrt{3}$$

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

$$9\times 2\sqrt{3}-10\sqrt{6}\sqrt{3}$$

Multiply 9 and 2 to get 18.

$$18\sqrt{3}-10\sqrt{6}\sqrt{3}$$

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}.

$$18\sqrt{3}-10\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$18\sqrt{3}-10\times 3\sqrt{2}$$

Multiply -10 and 3 to get -30.

$$18\sqrt{3}-30\sqrt{2}$$