Solve sqrt{18}+sqrt{8}-frac{sqrt{6}*sqrt{2}}{sqrt{3}}

$$\sqrt{ 18 } + \sqrt{ 8 } - \frac{ \sqrt{ 6 } \times \sqrt{ 2 } }{ \sqrt{ 3 } }$$

Evaluate

$$5\sqrt{2}-2\approx 5.071067812$$

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}.

$$3\sqrt{2}+\sqrt{8}-\frac{\sqrt{6}\sqrt{2}}{\sqrt{3}}$$

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}.

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

Combine 3\sqrt{2} and 2\sqrt{2} to get 5\sqrt{2}.

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

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}.

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

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

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

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$5\sqrt{2}-\frac{2\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

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

Multiply 2 and 3 to get 6.

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

Divide 6 by 3 to get 2.

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