Solve 3sqrt{32}-5sqrt{3}*sqrt{6}=

$$3 \sqrt{ 32 } -5 \sqrt{ 3 } \times \sqrt{ 6 } =$$

Evaluate

$$-3\sqrt{2}\approx -4.242640687$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$3\times 4\sqrt{2}-5\sqrt{3}\sqrt{6}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{2}-5\sqrt{3}\sqrt{6}$$

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}.

$$12\sqrt{2}-5\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$12\sqrt{2}-5\times 3\sqrt{2}$$

Multiply 5 and 3 to get 15.

$$12\sqrt{2}-15\sqrt{2}$$

Combine 12\sqrt{2} and -15\sqrt{2} to get -3\sqrt{2}.

$$-3\sqrt{2}$$