Solve 2/1/sqrt{4}+sqrt{(1/4)^2+5(3/4)^3*(frac{2}{3})^2}

$$\frac { \frac { 2 } { 1 } } { \sqrt { 4 } } + \sqrt { ( \frac { 1 } { 4 } ) ^ { 2 } + 5 ( \frac { 3 } { 4 } ) ^ { 3 } \cdot ( \frac { 2 } { 3 } ) ^ { 2 } }$$

Evaluate

$$2$$

Solution Steps

Anything divided by one gives itself.

$$\frac{2}{\sqrt{4}}+\sqrt{\left(\frac{1}{4}\right)^{2}+5\times \left(\frac{3}{4}\right)^{3}\times \left(\frac{2}{3}\right)^{2}}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{2}+\sqrt{\left(\frac{1}{4}\right)^{2}+5\times \left(\frac{3}{4}\right)^{3}\times \left(\frac{2}{3}\right)^{2}}$$

Divide 2 by 2 to get 1.

$$1+\sqrt{\left(\frac{1}{4}\right)^{2}+5\times \left(\frac{3}{4}\right)^{3}\times \left(\frac{2}{3}\right)^{2}}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$1+\sqrt{\frac{1}{16}+5\times \left(\frac{3}{4}\right)^{3}\times \left(\frac{2}{3}\right)^{2}}$$

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$1+\sqrt{\frac{1}{16}+5\times \frac{27}{64}\times \left(\frac{2}{3}\right)^{2}}$$

Express 5\times \frac{27}{64} as a single fraction.

$$1+\sqrt{\frac{1}{16}+\frac{5\times 27}{64}\times \left(\frac{2}{3}\right)^{2}}$$

Multiply 5 and 27 to get 135.

$$1+\sqrt{\frac{1}{16}+\frac{135}{64}\times \left(\frac{2}{3}\right)^{2}}$$

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

$$1+\sqrt{\frac{1}{16}+\frac{135}{64}\times \frac{4}{9}}$$

Multiply \frac{135}{64} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$1+\sqrt{\frac{1}{16}+\frac{135\times 4}{64\times 9}}$$

Do the multiplications in the fraction \frac{135\times 4}{64\times 9}.

$$1+\sqrt{\frac{1}{16}+\frac{540}{576}}$$

Reduce the fraction \frac{540}{576} to lowest terms by extracting and canceling out 36.

$$1+\sqrt{\frac{1}{16}+\frac{15}{16}}$$

Since \frac{1}{16} and \frac{15}{16} have the same denominator, add them by adding their numerators.

$$1+\sqrt{\frac{1+15}{16}}$$

Add 1 and 15 to get 16.

$$1+\sqrt{\frac{16}{16}}$$

Divide 16 by 16 to get 1.

$$1+\sqrt{1}$$

Calculate the square root of 1 and get 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$