Solve sqrt{1/8/2}+sqrt{2/frac{1{8}}}-2

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

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Express \frac{\frac{1}{8}}{2} as a single fraction.

$$\sqrt{\frac{1}{8\times 2}}+\sqrt{\frac{2}{\frac{1}{8}}}-2$$

Multiply 8 and 2 to get 16.

$$\sqrt{\frac{1}{16}}+\sqrt{\frac{2}{\frac{1}{8}}}-2$$

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{1}{4}+\sqrt{\frac{2}{\frac{1}{8}}}-2$$

Divide 2 by \frac{1}{8} by multiplying 2 by the reciprocal of \frac{1}{8}.

$$\frac{1}{4}+\sqrt{2\times 8}-2$$

Multiply 2 and 8 to get 16.

$$\frac{1}{4}+\sqrt{16}-2$$

Calculate the square root of 16 and get 4.

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

Convert 4 to fraction \frac{16}{4}.

$$\frac{1}{4}+\frac{16}{4}-2$$

Since \frac{1}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+16}{4}-2$$

Add 1 and 16 to get 17.

$$\frac{17}{4}-2$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{17}{4}-\frac{8}{4}$$

Since \frac{17}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-8}{4}$$

Subtract 8 from 17 to get 9.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$