Solve sqrt{0.9^2/36+0.8^2/49}

$$\sqrt{ \frac{ { 0.9 }^{ 2 } }{ 36 } + \frac{ { 0.8 }^{ 2 } }{ 49 } }$$

Evaluate

$$\frac{\sqrt{697}}{140}\approx 0.18857684$$

Solution Steps

Calculate 0.9 to the power of 2 and get 0.81.

$$\sqrt{\frac{0.81}{36}+\frac{0.8^{2}}{49}}$$

Expand \frac{0.81}{36} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{81}{3600}+\frac{0.8^{2}}{49}}$$

Reduce the fraction \frac{81}{3600} to lowest terms by extracting and canceling out 9.

$$\sqrt{\frac{9}{400}+\frac{0.8^{2}}{49}}$$

Calculate 0.8 to the power of 2 and get 0.64.

$$\sqrt{\frac{9}{400}+\frac{0.64}{49}}$$

Expand \frac{0.64}{49} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{9}{400}+\frac{64}{4900}}$$

Reduce the fraction \frac{64}{4900} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{9}{400}+\frac{16}{1225}}$$

Least common multiple of 400 and 1225 is 19600. Convert \frac{9}{400} and \frac{16}{1225} to fractions with denominator 19600.

$$\sqrt{\frac{441}{19600}+\frac{256}{19600}}$$

Since \frac{441}{19600} and \frac{256}{19600} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{441+256}{19600}}$$

Add 441 and 256 to get 697.

$$\sqrt{\frac{697}{19600}}$$

Rewrite the square root of the division \sqrt{\frac{697}{19600}} as the division of square roots \frac{\sqrt{697}}{\sqrt{19600}}.

$$\frac{\sqrt{697}}{\sqrt{19600}}$$

Calculate the square root of 19600 and get 140.

$$\frac{\sqrt{697}}{140}$$