Solve sqrt{6*0.807+6*0.781/12}

$$\sqrt{ \frac{ 6 \times 0.807+6 \times 0.781 }{ 12 } }$$

Evaluate

$$\frac{\sqrt{1985}}{50}\approx 0.891066776$$

Solution Steps

Multiply 6 and 0.807 to get 4.842.

$$\sqrt{\frac{4.842+6\times 0.781}{12}}$$

Multiply 6 and 0.781 to get 4.686.

$$\sqrt{\frac{4.842+4.686}{12}}$$

Add 4.842 and 4.686 to get 9.528.

$$\sqrt{\frac{9.528}{12}}$$

Expand \frac{9.528}{12} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{9528}{12000}}$$

Reduce the fraction \frac{9528}{12000} to lowest terms by extracting and canceling out 24.

$$\sqrt{\frac{397}{500}}$$

Rewrite the square root of the division \sqrt{\frac{397}{500}} as the division of square roots \frac{\sqrt{397}}{\sqrt{500}}.

$$\frac{\sqrt{397}}{\sqrt{500}}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$\frac{\sqrt{397}}{10\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{397}}{10\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{397}\sqrt{5}}{10\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{397}\sqrt{5}}{10\times 5}$$

To multiply \sqrt{397} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{1985}}{10\times 5}$$

Multiply 10 and 5 to get 50.

$$\frac{\sqrt{1985}}{50}$$