Solve sqrt{6}*(3sqrt{7}-5sqrt{3})

$$\sqrt { 6 } \cdot ( 3 \sqrt { 7 } - 5 \sqrt { 3 } )$$

Evaluate

$$3\sqrt{2}\left(\sqrt{21}-5\right)\approx -1.77098134$$

Solution Steps

Use the distributive property to multiply \sqrt{6} by 3\sqrt{7}-5\sqrt{3}.

$$3\sqrt{6}\sqrt{7}-5\sqrt{6}\sqrt{3}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$3\sqrt{42}-5\sqrt{6}\sqrt{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$3\sqrt{42}-5\sqrt{3}\sqrt{2}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\sqrt{42}-5\times 3\sqrt{2}$$

Multiply -5 and 3 to get -15.

$$3\sqrt{42}-15\sqrt{2}$$

Factor

$$3 \sqrt{2} {(\sqrt{21} - 5)} = -1.77098134$$