Solve 3*sqrt{18}+1/5sqrt{50}-4*sqrt{1/2}

$$3 \times \sqrt { 18 } + \frac { 1 } { 5 } \sqrt { 50 } - 4 \times \sqrt { \frac { 1 } { 2 } }$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

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}.

$$3\times 3\sqrt{2}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}+\frac{1}{5}\sqrt{50}-4\sqrt{\frac{1}{2}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$9\sqrt{2}+\frac{1}{5}\times 5\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Cancel out 5 and 5.

$$9\sqrt{2}+\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Combine 9\sqrt{2} and \sqrt{2} to get 10\sqrt{2}.

$$10\sqrt{2}-4\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$10\sqrt{2}-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$10\sqrt{2}-4\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$10\sqrt{2}-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$10\sqrt{2}-4\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$10\sqrt{2}-2\sqrt{2}$$

Combine 10\sqrt{2} and -2\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}$$