Solve sqrt{4*1.3*6956/3.14*135.3}

$$\sqrt{ \frac{ 4 \times 1.3 \times 6956 }{ 3.14 \times 135.3 } }$$

Evaluate

$$\frac{20\sqrt{9604403094}}{212421}\approx 9.227153302$$

Solution Steps

Multiply 4 and 1.3 to get 5.2.

$$\sqrt{\frac{5.2\times 6956}{3.14\times 135.3}}$$

Multiply 5.2 and 6956 to get 36171.2.

$$\sqrt{\frac{36171.2}{3.14\times 135.3}}$$

Multiply 3.14 and 135.3 to get 424.842.

$$\sqrt{\frac{36171.2}{424.842}}$$

Expand \frac{36171.2}{424.842} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{36171200}{424842}}$$

Reduce the fraction \frac{36171200}{424842} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{18085600}{212421}}$$

Rewrite the square root of the division \sqrt{\frac{18085600}{212421}} as the division of square roots \frac{\sqrt{18085600}}{\sqrt{212421}}.

$$\frac{\sqrt{18085600}}{\sqrt{212421}}$$

Factor 18085600=20^{2}\times 45214. Rewrite the square root of the product \sqrt{20^{2}\times 45214} as the product of square roots \sqrt{20^{2}}\sqrt{45214}. Take the square root of 20^{2}.

$$\frac{20\sqrt{45214}}{\sqrt{212421}}$$

Rationalize the denominator of \frac{20\sqrt{45214}}{\sqrt{212421}} by multiplying numerator and denominator by \sqrt{212421}.

$$\frac{20\sqrt{45214}\sqrt{212421}}{\left(\sqrt{212421}\right)^{2}}$$

The square of \sqrt{212421} is 212421.

$$\frac{20\sqrt{45214}\sqrt{212421}}{212421}$$

To multiply \sqrt{45214} and \sqrt{212421}, multiply the numbers under the square root.

$$\frac{20\sqrt{9604403094}}{212421}$$