Solve {left(1+sqrt{frac{4/16}}{2}right)}^2+1+sqrt{frac{4/16}}{2}+3/16

$${ \left( \frac{ 1+ \sqrt{ \frac{ 4 }{ 16 } } }{ 2 } \right) }^{ 2 } + \frac{ 1+ \sqrt{ \frac{ 4 }{ 16 } } }{ 2 } + \frac{ 3 }{ 16 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\left(\frac{1+\sqrt{\frac{1}{4}}}{2}\right)^{2}+\frac{1+\sqrt{\frac{4}{16}}}{2}+\frac{3}{16}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\left(\frac{1+\frac{1}{2}}{2}\right)^{2}+\frac{1+\sqrt{\frac{4}{16}}}{2}+\frac{3}{16}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\left(\frac{\frac{3}{2}}{2}\right)^{2}+\frac{1+\sqrt{\frac{4}{16}}}{2}+\frac{3}{16}$$

Express \frac{\frac{3}{2}}{2} as a single fraction.

$$\left(\frac{3}{2\times 2}\right)^{2}+\frac{1+\sqrt{\frac{4}{16}}}{2}+\frac{3}{16}$$

Multiply 2 and 2 to get 4.

$$\left(\frac{3}{4}\right)^{2}+\frac{1+\sqrt{\frac{4}{16}}}{2}+\frac{3}{16}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{9}{16}+\frac{1+\sqrt{\frac{4}{16}}}{2}+\frac{3}{16}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{9}{16}+\frac{1+\sqrt{\frac{1}{4}}}{2}+\frac{3}{16}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{9}{16}+\frac{1+\frac{1}{2}}{2}+\frac{3}{16}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{9}{16}+\frac{\frac{3}{2}}{2}+\frac{3}{16}$$

Express \frac{\frac{3}{2}}{2} as a single fraction.

$$\frac{9}{16}+\frac{3}{2\times 2}+\frac{3}{16}$$

Multiply 2 and 2 to get 4.

$$\frac{9}{16}+\frac{3}{4}+\frac{3}{16}$$

Add \frac{9}{16} and \frac{3}{4} to get \frac{21}{16}.

$$\frac{21}{16}+\frac{3}{16}$$

Add \frac{21}{16} and \frac{3}{16} to get \frac{3}{2}.

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

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$