Solve {r}{sqrt{4996280933874}}{*266^2div(sqrt{466}*8)}

$$\left. \begin{array} { r } { \sqrt { 4996280933874 } } \\ { \times 266 ^ { 2 } \div ( \sqrt { 466 } \times 8 ) } \end{array} \right.$$

Evaluate

$$\frac{53067\sqrt{64674080977369}}{466}\approx 915806566.14381659$$

Solution Steps

Factor 4996280933874=3^{2}\times 555142325986. Rewrite the square root of the product \sqrt{3^{2}\times 555142325986} as the product of square roots \sqrt{3^{2}}\sqrt{555142325986}. Take the square root of 3^{2}.

$$\frac{3\sqrt{555142325986}\times 266^{2}}{8\sqrt{466}}$$

Calculate 266 to the power of 2 and get 70756.

$$\frac{3\sqrt{555142325986}\times 70756}{8\sqrt{466}}$$

Multiply 3 and 70756 to get 212268.

$$\frac{212268\sqrt{555142325986}}{8\sqrt{466}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{53067\sqrt{555142325986}}{2\sqrt{466}}$$

Rationalize the denominator of \frac{53067\sqrt{555142325986}}{2\sqrt{466}} by multiplying numerator and denominator by \sqrt{466}.

$$\frac{53067\sqrt{555142325986}\sqrt{466}}{2\left(\sqrt{466}\right)^{2}}$$

The square of \sqrt{466} is 466.

$$\frac{53067\sqrt{555142325986}\sqrt{466}}{2\times 466}$$

To multiply \sqrt{555142325986} and \sqrt{466}, multiply the numbers under the square root.

$$\frac{53067\sqrt{258696323909476}}{2\times 466}$$

Multiply 2 and 466 to get 932.

$$\frac{53067\sqrt{258696323909476}}{932}$$

Factor 258696323909476=2^{2}\times 64674080977369. Rewrite the square root of the product \sqrt{2^{2}\times 64674080977369} as the product of square roots \sqrt{2^{2}}\sqrt{64674080977369}. Take the square root of 2^{2}.

$$\frac{53067\times 2\sqrt{64674080977369}}{932}$$

Multiply 53067 and 2 to get 106134.

$$\frac{106134\sqrt{64674080977369}}{932}$$

Divide 106134\sqrt{64674080977369} by 932 to get \frac{53067}{466}\sqrt{64674080977369}.

$$\frac{53067}{466}\sqrt{64674080977369}$$