Solve sqrt{(1.82)^2/25+(1.51)^2/25}

$$\sqrt { \frac { ( 1.82 ) ^ { 2 } } { 25 } + \frac { ( 1.51 ) ^ { 2 } } { 25 } }$$

Evaluate

$$\frac{\sqrt{2237}}{100}\approx 0.472969344$$

Solution Steps

Calculate 1.82 to the power of 2 and get 3.3124.

$$\sqrt{\frac{3.3124}{25}+\frac{1.51^{2}}{25}}$$

Expand \frac{3.3124}{25} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{33124}{250000}+\frac{1.51^{2}}{25}}$$

Reduce the fraction \frac{33124}{250000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{8281}{62500}+\frac{1.51^{2}}{25}}$$

Calculate 1.51 to the power of 2 and get 2.2801.

$$\sqrt{\frac{8281}{62500}+\frac{2.2801}{25}}$$

Expand \frac{2.2801}{25} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{8281}{62500}+\frac{22801}{250000}}$$

Least common multiple of 62500 and 250000 is 250000. Convert \frac{8281}{62500} and \frac{22801}{250000} to fractions with denominator 250000.

$$\sqrt{\frac{33124}{250000}+\frac{22801}{250000}}$$

Since \frac{33124}{250000} and \frac{22801}{250000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{33124+22801}{250000}}$$

Add 33124 and 22801 to get 55925.

$$\sqrt{\frac{55925}{250000}}$$

Reduce the fraction \frac{55925}{250000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{2237}{10000}}$$

Rewrite the square root of the division \sqrt{\frac{2237}{10000}} as the division of square roots \frac{\sqrt{2237}}{\sqrt{10000}}.

$$\frac{\sqrt{2237}}{\sqrt{10000}}$$

Calculate the square root of 10000 and get 100.

$$\frac{\sqrt{2237}}{100}$$