Solve 1/2sqrt{18}-6sqrt{32}

$$\frac { 1 } { 2 } \sqrt { 18 } - 6 \sqrt { 32 }$$

Evaluate

$$-\frac{45\sqrt{2}}{2}\approx -31.819805153$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{1}{2}\times 3\sqrt{2}-6\sqrt{32}$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{3}{2}\sqrt{2}-6\sqrt{32}$$

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}.

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

Multiply -6 and 4 to get -24.

$$\frac{3}{2}\sqrt{2}-24\sqrt{2}$$

Combine \frac{3}{2}\sqrt{2} and -24\sqrt{2} to get -\frac{45}{2}\sqrt{2}.

$$-\frac{45}{2}\sqrt{2}$$