Solve 2sqrt{21}*5sqrt{2}*sqrt{7}

$$2 \sqrt { 21 } \cdot 5 \sqrt { 2 } \cdot \sqrt { 7 }$$

Evaluate

$$70\sqrt{6}\approx 171.464281995$$

Solution Steps

Factor 21=7\times 3. Rewrite the square root of the product \sqrt{7\times 3} as the product of square roots \sqrt{7}\sqrt{3}.

$$2\times 5\sqrt{7}\sqrt{3}\sqrt{2}\sqrt{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$2\times 5\times 7\sqrt{2}\sqrt{3}$$

Multiply 2 and 5 to get 10.

$$10\times 7\sqrt{2}\sqrt{3}$$

Multiply 10 and 7 to get 70.

$$70\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$70\sqrt{6}$$