Solve {l}{sqrt{114*78*39}}{*sqrt{74}}

$$\left. \begin{array} { l } { \sqrt { 114 \times 78 \times 39 } } \\ { \times \sqrt { 74 } } \end{array} \right.$$

Evaluate

$$78\sqrt{4218}\approx 5065.798258912$$

Solution Steps

Multiply 114 and 78 to get 8892.

$$\sqrt{8892\times 39}\sqrt{74}$$

Multiply 8892 and 39 to get 346788.

$$\sqrt{346788}\sqrt{74}$$

Factor 346788=78^{2}\times 57. Rewrite the square root of the product \sqrt{78^{2}\times 57} as the product of square roots \sqrt{78^{2}}\sqrt{57}. Take the square root of 78^{2}.

$$78\sqrt{57}\sqrt{74}$$

To multiply \sqrt{57} and \sqrt{74}, multiply the numbers under the square root.

$$78\sqrt{4218}$$