Solve 15-2*sqrt{3}*sqrt{12}*1/2

$$15-2 \times \sqrt{ 3 } \times \sqrt{ 12 } \times \frac{ 1 }{ 2 }$$

Evaluate

$$9$$

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$15-2\sqrt{3}\sqrt{3}\sqrt{4}\times \frac{1}{2}$$

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

$$15-2\times 3\sqrt{4}\times \frac{1}{2}$$

Multiply 2 and 3 to get 6.

$$15-6\sqrt{4}\times \frac{1}{2}$$

Calculate the square root of 4 and get 2.

$$15-6\times 2\times \frac{1}{2}$$

Multiply 6 and 2 to get 12.

$$15-12\times \frac{1}{2}$$

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

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

Divide 12 by 2 to get 6.

$$15-6$$

Subtract 6 from 15 to get 9.

$$9$$

Factor

$$3^{2}$$