Solve sqrt{10left(1-2right)+6left(2-2right)+4left(4-2right)+2left(5-2right)+(8-2)/28}

$$\sqrt{ \frac{ 10 \left( 1-2 \right) +6 \left( 2-2 \right) +4 \left( 4-2 \right) +2 \left( 5-2 \right) +(8-2) }{ 28 } }$$

Evaluate

$$\frac{\sqrt{70}}{14}\approx 0.597614305$$

Solution Steps

Subtract 2 from 1 to get -1.

$$\sqrt{\frac{10\left(-1\right)+6\left(2-2\right)+4\left(4-2\right)+2\left(5-2\right)+8-2}{28}}$$

Multiply 10 and -1 to get -10.

$$\sqrt{\frac{-10+6\left(2-2\right)+4\left(4-2\right)+2\left(5-2\right)+8-2}{28}}$$

Subtract 2 from 2 to get 0.

$$\sqrt{\frac{-10+6\times 0+4\left(4-2\right)+2\left(5-2\right)+8-2}{28}}$$

Multiply 6 and 0 to get 0.

$$\sqrt{\frac{-10+0+4\left(4-2\right)+2\left(5-2\right)+8-2}{28}}$$

Add -10 and 0 to get -10.

$$\sqrt{\frac{-10+4\left(4-2\right)+2\left(5-2\right)+8-2}{28}}$$

Subtract 2 from 4 to get 2.

$$\sqrt{\frac{-10+4\times 2+2\left(5-2\right)+8-2}{28}}$$

Multiply 4 and 2 to get 8.

$$\sqrt{\frac{-10+8+2\left(5-2\right)+8-2}{28}}$$

Add -10 and 8 to get -2.

$$\sqrt{\frac{-2+2\left(5-2\right)+8-2}{28}}$$

Subtract 2 from 5 to get 3.

$$\sqrt{\frac{-2+2\times 3+8-2}{28}}$$

Multiply 2 and 3 to get 6.

$$\sqrt{\frac{-2+6+8-2}{28}}$$

Add -2 and 6 to get 4.

$$\sqrt{\frac{4+8-2}{28}}$$

Add 4 and 8 to get 12.

$$\sqrt{\frac{12-2}{28}}$$

Subtract 2 from 12 to get 10.

$$\sqrt{\frac{10}{28}}$$

Reduce the fraction \frac{10}{28} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{5}{14}}$$

Rewrite the square root of the division \sqrt{\frac{5}{14}} as the division of square roots \frac{\sqrt{5}}{\sqrt{14}}.

$$\frac{\sqrt{5}}{\sqrt{14}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{5}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{5}\sqrt{14}}{14}$$

To multiply \sqrt{5} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{70}}{14}$$