Solve sqrt{34.2div10}

$$\sqrt{ 34.2 \div 10 }$$

Evaluate

$$\frac{3\sqrt{38}}{10}\approx 1.849324201$$

Solution Steps

Expand \frac{34.2}{10} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{342}{100}}$$

Reduce the fraction \frac{342}{100} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{171}{50}}$$

Rewrite the square root of the division \sqrt{\frac{171}{50}} as the division of square roots \frac{\sqrt{171}}{\sqrt{50}}.

$$\frac{\sqrt{171}}{\sqrt{50}}$$

Factor 171=3^{2}\times 19. Rewrite the square root of the product \sqrt{3^{2}\times 19} as the product of square roots \sqrt{3^{2}}\sqrt{19}. Take the square root of 3^{2}.

$$\frac{3\sqrt{19}}{\sqrt{50}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{3\sqrt{19}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{3\sqrt{19}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{19}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{19}\sqrt{2}}{5\times 2}$$

To multiply \sqrt{19} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{3\sqrt{38}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{3\sqrt{38}}{10}$$