Solve sqrt{56}*5sqrt{6}

$$\sqrt { 56 } \times 5 \sqrt { 6 }$$

Evaluate

$$20\sqrt{21}\approx 91.651513899$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$5\times 2\sqrt{14}\sqrt{6}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{14}\sqrt{6}$$

To multiply \sqrt{14} and \sqrt{6}, multiply the numbers under the square root.

$$10\sqrt{84}$$

Factor 84=2^{2}\times 21. Rewrite the square root of the product \sqrt{2^{2}\times 21} as the product of square roots \sqrt{2^{2}}\sqrt{21}. Take the square root of 2^{2}.

$$10\times 2\sqrt{21}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{21}$$