Solve sqrt{0.01+0.09+0.01+0.09+0.04/7*6}

$$\sqrt{ \frac{ 0.01+0.09+0.01+0.09+0.04 }{ 7 \times 6 } }$$

Evaluate

$$\frac{\sqrt{7}}{35}\approx 0.075592895$$

Solution Steps

Add 0.01 and 0.09 to get 0.1.

$$\sqrt{\frac{0.1+0.01+0.09+0.04}{7\times 6}}$$

Add 0.1 and 0.01 to get 0.11.

$$\sqrt{\frac{0.11+0.09+0.04}{7\times 6}}$$

Add 0.11 and 0.09 to get 0.2.

$$\sqrt{\frac{0.2+0.04}{7\times 6}}$$

Add 0.2 and 0.04 to get 0.24.

$$\sqrt{\frac{0.24}{7\times 6}}$$

Multiply 7 and 6 to get 42.

$$\sqrt{\frac{0.24}{42}}$$

Expand \frac{0.24}{42} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{24}{4200}}$$

Reduce the fraction \frac{24}{4200} to lowest terms by extracting and canceling out 24.

$$\sqrt{\frac{1}{175}}$$

Rewrite the square root of the division \sqrt{\frac{1}{175}} as the division of square roots \frac{\sqrt{1}}{\sqrt{175}}.

$$\frac{\sqrt{1}}{\sqrt{175}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{175}}$$

Factor 175=5^{2}\times 7. Rewrite the square root of the product \sqrt{5^{2}\times 7} as the product of square roots \sqrt{5^{2}}\sqrt{7}. Take the square root of 5^{2}.

$$\frac{1}{5\sqrt{7}}$$

Rationalize the denominator of \frac{1}{5\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{7}}{5\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{7}}{5\times 7}$$

Multiply 5 and 7 to get 35.

$$\frac{\sqrt{7}}{35}$$