Solve sqrt{3*273*8.31div29}

$$\sqrt{ 3 \times 273 \times 8.31 \div 29 }$$

Evaluate

$$\frac{3\sqrt{2193009}}{290}\approx 15.319460241$$

Solution Steps

Multiply 3 and 273 to get 819.

$$\sqrt{\frac{819\times 8.31}{29}}$$

Multiply 819 and 8.31 to get 6805.89.

$$\sqrt{\frac{6805.89}{29}}$$

Expand \frac{6805.89}{29} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{680589}{2900}}$$

Rewrite the square root of the division \sqrt{\frac{680589}{2900}} as the division of square roots \frac{\sqrt{680589}}{\sqrt{2900}}.

$$\frac{\sqrt{680589}}{\sqrt{2900}}$$

Factor 680589=3^{2}\times 75621. Rewrite the square root of the product \sqrt{3^{2}\times 75621} as the product of square roots \sqrt{3^{2}}\sqrt{75621}. Take the square root of 3^{2}.

$$\frac{3\sqrt{75621}}{\sqrt{2900}}$$

Factor 2900=10^{2}\times 29. Rewrite the square root of the product \sqrt{10^{2}\times 29} as the product of square roots \sqrt{10^{2}}\sqrt{29}. Take the square root of 10^{2}.

$$\frac{3\sqrt{75621}}{10\sqrt{29}}$$

Rationalize the denominator of \frac{3\sqrt{75621}}{10\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$\frac{3\sqrt{75621}\sqrt{29}}{10\left(\sqrt{29}\right)^{2}}$$

The square of \sqrt{29} is 29.

$$\frac{3\sqrt{75621}\sqrt{29}}{10\times 29}$$

To multiply \sqrt{75621} and \sqrt{29}, multiply the numbers under the square root.

$$\frac{3\sqrt{2193009}}{10\times 29}$$

Multiply 10 and 29 to get 290.

$$\frac{3\sqrt{2193009}}{290}$$