Solve 3sqrt{8}-3sqrt{27}+1/2

$$3 \sqrt { 8 } - 3 \sqrt { 27 } + \frac { 1 } { 2 }$$

Evaluate

$$6\sqrt{2}+\frac{1}{2}-9\sqrt{3}\approx -6.603175894$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$3\times 2\sqrt{2}-3\sqrt{27}+\frac{1}{2}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}-3\sqrt{27}+\frac{1}{2}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

Multiply -3 and 3 to get -9.

$$6\sqrt{2}-9\sqrt{3}+\frac{1}{2}$$

Factor

$$\frac{12 \sqrt{2} + 1 - 18 \sqrt{3}}{2} = -6.603175893881323$$