Solve 7sqrt{2/49}-3sqrt{8/81}+sqrt{18/36}approx

$$7 \sqrt { \frac { 2 } { 49 } } - 3 \sqrt { \frac { 8 } { 81 } } + \sqrt { \frac { 18 } { 36 } } \approx$$

Evaluate

$$\frac{5\sqrt{2}}{6}\approx 1.178511302$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{49}} as the division of square roots \frac{\sqrt{2}}{\sqrt{49}}.

$$7\times \frac{\sqrt{2}}{\sqrt{49}}-3\sqrt{\frac{8}{81}}+\sqrt{\frac{18}{36}}$$

Calculate the square root of 49 and get 7.

$$7\times \frac{\sqrt{2}}{7}-3\sqrt{\frac{8}{81}}+\sqrt{\frac{18}{36}}$$

Cancel out 7 and 7.

$$\sqrt{2}-3\sqrt{\frac{8}{81}}+\sqrt{\frac{18}{36}}$$

Rewrite the square root of the division \sqrt{\frac{8}{81}} as the division of square roots \frac{\sqrt{8}}{\sqrt{81}}.

$$\sqrt{2}-3\times \frac{\sqrt{8}}{\sqrt{81}}+\sqrt{\frac{18}{36}}$$

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}.

$$\sqrt{2}-3\times \frac{2\sqrt{2}}{\sqrt{81}}+\sqrt{\frac{18}{36}}$$

Calculate the square root of 81 and get 9.

$$\sqrt{2}-3\times \frac{2\sqrt{2}}{9}+\sqrt{\frac{18}{36}}$$

Cancel out 9, the greatest common factor in 3 and 9.

$$\sqrt{2}+\frac{2\sqrt{2}}{-3}+\sqrt{\frac{18}{36}}$$

Combine \sqrt{2} and \frac{2\sqrt{2}}{-3} to get \frac{1}{3}\sqrt{2}.

$$\frac{1}{3}\sqrt{2}+\sqrt{\frac{18}{36}}$$

Reduce the fraction \frac{18}{36} to lowest terms by extracting and canceling out 18.

$$\frac{1}{3}\sqrt{2}+\sqrt{\frac{1}{2}}$$

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

$$\frac{1}{3}\sqrt{2}+\frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{3}\sqrt{2}+\frac{1}{\sqrt{2}}$$

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

$$\frac{1}{3}\sqrt{2}+\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1}{3}\sqrt{2}+\frac{\sqrt{2}}{2}$$

Combine \frac{1}{3}\sqrt{2} and \frac{\sqrt{2}}{2} to get \frac{5}{6}\sqrt{2}.

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