Solve 2/sqrt{1+frac{1{4}+1}*sqrt{4}}

$$\frac { 2 } { \sqrt { 1 + \frac { 1 } { 4 } + 1 } \times \sqrt { 4 } }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

$$\frac{2}{\sqrt{\frac{5}{4}+1}\sqrt{4}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{2}{\sqrt{\frac{5}{4}+\frac{4}{4}}\sqrt{4}}$$

Since \frac{5}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{\sqrt{\frac{5+4}{4}}\sqrt{4}}$$

Add 5 and 4 to get 9.

$$\frac{2}{\sqrt{\frac{9}{4}}\sqrt{4}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{2}{\frac{3}{2}\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{\frac{3}{2}\times 2}$$

Cancel out 2 and 2.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$