Solve sqrt{(0.97/71.02)^2+(2*0.17/83.87)^2}

$$\sqrt { ( \frac { 0.97 } { 71.02 } ) ^ { 2 } + ( \frac { 2 \times 0.17 } { 83.87 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{720152499545}}{59564474}\approx 0.014247049$$

Solution Steps

Expand \frac{0.97}{71.02} by multiplying both numerator and the denominator by 100.

$$\sqrt{\left(\frac{97}{7102}\right)^{2}+\left(\frac{2\times 0.17}{83.87}\right)^{2}}$$

Calculate \frac{97}{7102} to the power of 2 and get \frac{9409}{50438404}.

$$\sqrt{\frac{9409}{50438404}+\left(\frac{2\times 0.17}{83.87}\right)^{2}}$$

Multiply 2 and 0.17 to get 0.34.

$$\sqrt{\frac{9409}{50438404}+\left(\frac{0.34}{83.87}\right)^{2}}$$

Expand \frac{0.34}{83.87} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{9409}{50438404}+\left(\frac{34}{8387}\right)^{2}}$$

Calculate \frac{34}{8387} to the power of 2 and get \frac{1156}{70341769}.

$$\sqrt{\frac{9409}{50438404}+\frac{1156}{70341769}}$$

Add \frac{9409}{50438404} and \frac{1156}{70341769} to get \frac{720152499545}{3547926562896676}.

$$\sqrt{\frac{720152499545}{3547926562896676}}$$

Rewrite the square root of the division \sqrt{\frac{720152499545}{3547926562896676}} as the division of square roots \frac{\sqrt{720152499545}}{\sqrt{3547926562896676}}.

$$\frac{\sqrt{720152499545}}{\sqrt{3547926562896676}}$$

Calculate the square root of 3547926562896676 and get 59564474.

$$\frac{\sqrt{720152499545}}{59564474}$$