Solve 1/2|0|+1|5/sqrt{frac{12^2+1^2}}

$$\frac { \frac { 1 } { 2 } | 0 | + 1 | 5 } { \sqrt { \frac { 1 } { 2 } ^ { 2 } + 1 ^ { 2 } } }$$

Evaluate

$$2\sqrt{5}\approx 4.472135955$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$\frac{1}{2}\times 0+\frac{1|5|}{\sqrt{\left(\frac{1}{2}\right)^{2}+1^{2}}}$$

Multiply \frac{1}{2} and 0 to get 0.

$$0+\frac{1|5|}{\sqrt{\left(\frac{1}{2}\right)^{2}+1^{2}}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 5 is 5.

$$0+\frac{1\times 5}{\sqrt{\left(\frac{1}{2}\right)^{2}+1^{2}}}$$

Multiply 1 and 5 to get 5.

$$0+\frac{5}{\sqrt{\left(\frac{1}{2}\right)^{2}+1^{2}}}$$

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

$$0+\frac{5}{\sqrt{\frac{1}{4}+1^{2}}}$$

Calculate 1 to the power of 2 and get 1.

$$0+\frac{5}{\sqrt{\frac{1}{4}+1}}$$

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

$$0+\frac{5}{\sqrt{\frac{1}{4}+\frac{4}{4}}}$$

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

$$0+\frac{5}{\sqrt{\frac{1+4}{4}}}$$

Add 1 and 4 to get 5.

$$0+\frac{5}{\sqrt{\frac{5}{4}}}$$

Rewrite the square root of the division \sqrt{\frac{5}{4}} as the division of square roots \frac{\sqrt{5}}{\sqrt{4}}.

$$0+\frac{5}{\frac{\sqrt{5}}{\sqrt{4}}}$$

Calculate the square root of 4 and get 2.

$$0+\frac{5}{\frac{\sqrt{5}}{2}}$$

Divide 5 by \frac{\sqrt{5}}{2} by multiplying 5 by the reciprocal of \frac{\sqrt{5}}{2}.

$$0+\frac{5\times 2}{\sqrt{5}}$$

Rationalize the denominator of \frac{5\times 2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$0+\frac{5\times 2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$0+\frac{5\times 2\sqrt{5}}{5}$$

Multiply 5 and 2 to get 10.

$$0+\frac{10\sqrt{5}}{5}$$

Divide 10\sqrt{5} by 5 to get 2\sqrt{5}.

$$0+2\sqrt{5}$$

Anything plus zero gives itself.

$$2\sqrt{5}$$