Solve sqrt{(1.6/2)^2+(3/2)^2}=

$$\sqrt { ( \frac { 1.6 } { 2 } ) ^ { 2 } + ( \frac { 3 } { 2 } ) ^ { 2 } } =$$

Evaluate

$$1.7$$

Solution Steps

Expand \frac{1.6}{2} by multiplying both numerator and the denominator by 10.

$$\sqrt{\left(\frac{16}{20}\right)^{2}+\left(\frac{3}{2}\right)^{2}}$$

Reduce the fraction \frac{16}{20} to lowest terms by extracting and canceling out 4.

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

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$\sqrt{\frac{16}{25}+\left(\frac{3}{2}\right)^{2}}$$

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

$$\sqrt{\frac{16}{25}+\frac{9}{4}}$$

Add \frac{16}{25} and \frac{9}{4} to get \frac{289}{100}.

$$\sqrt{\frac{289}{100}}$$

Rewrite the square root of the division \frac{289}{100} as the division of square roots \frac{\sqrt{289}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{17}{10}$$

Factor

$$\frac{17}{2 \cdot 5} = 1\frac{7}{10} = 1.7$$