Solve 787divsqrt{542}div457*2454sqrt{21245}div271sqrt{666865925147}

$$787 \div \sqrt{ 542 } \div 457 \times 2454 \sqrt{ 21245 } \div 271 \sqrt{ 666865925147 }$$

Evaluate

$$\frac{965649\sqrt{7678821086223424130}}{33562537}\approx 79728168.49789837$$

Solution Steps

Express \frac{\frac{787}{\sqrt{542}}}{457} as a single fraction.

$$\frac{2454\times \frac{787}{\sqrt{542}\times 457}\sqrt{21245}}{271}\sqrt{666865925147}$$

Rationalize the denominator of \frac{787}{\sqrt{542}\times 457} by multiplying numerator and denominator by \sqrt{542}.

$$\frac{2454\times \frac{787\sqrt{542}}{\left(\sqrt{542}\right)^{2}\times 457}\sqrt{21245}}{271}\sqrt{666865925147}$$

The square of \sqrt{542} is 542.

$$\frac{2454\times \frac{787\sqrt{542}}{542\times 457}\sqrt{21245}}{271}\sqrt{666865925147}$$

Multiply 542 and 457 to get 247694.

$$\frac{2454\times \frac{787\sqrt{542}}{247694}\sqrt{21245}}{271}\sqrt{666865925147}$$

Express 2454\times \frac{787\sqrt{542}}{247694} as a single fraction.

$$\frac{\frac{2454\times 787\sqrt{542}}{247694}\sqrt{21245}}{271}\sqrt{666865925147}$$

Express \frac{2454\times 787\sqrt{542}}{247694}\sqrt{21245} as a single fraction.

$$\frac{\frac{2454\times 787\sqrt{542}\sqrt{21245}}{247694}}{271}\sqrt{666865925147}$$

Express \frac{\frac{2454\times 787\sqrt{542}\sqrt{21245}}{247694}}{271} as a single fraction.

$$\frac{2454\times 787\sqrt{542}\sqrt{21245}}{247694\times 271}\sqrt{666865925147}$$

Cancel out 2 in both numerator and denominator.

$$\frac{787\times 1227\sqrt{542}\sqrt{21245}}{271\times 123847}\sqrt{666865925147}$$

Multiply 787 and 1227 to get 965649.

$$\frac{965649\sqrt{542}\sqrt{21245}}{271\times 123847}\sqrt{666865925147}$$

To multiply \sqrt{542} and \sqrt{21245}, multiply the numbers under the square root.

$$\frac{965649\sqrt{11514790}}{271\times 123847}\sqrt{666865925147}$$

Multiply 271 and 123847 to get 33562537.

$$\frac{965649\sqrt{11514790}}{33562537}\sqrt{666865925147}$$

Express \frac{965649\sqrt{11514790}}{33562537}\sqrt{666865925147} as a single fraction.

$$\frac{965649\sqrt{11514790}\sqrt{666865925147}}{33562537}$$

To multiply \sqrt{11514790} and \sqrt{666865925147}, multiply the numbers under the square root.

$$\frac{965649\sqrt{7678821086223424130}}{33562537}$$