Solve 9sqrt{3}(sqrt{7}-sqrt{15})

$$9 \sqrt { 3 } ( \sqrt { 7 } - \sqrt { 15 } )$$

Evaluate

$$9\left(\sqrt{21}-3\sqrt{5}\right)\approx -19.130654138$$

Solution Steps

Use the distributive property to multiply 9\sqrt{3} by \sqrt{7}-\sqrt{15}.

$$9\sqrt{3}\sqrt{7}-9\sqrt{3}\sqrt{15}$$

To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.

$$9\sqrt{21}-9\sqrt{3}\sqrt{15}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$9\sqrt{21}-9\sqrt{3}\sqrt{3}\sqrt{5}$$

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

$$9\sqrt{21}-9\times 3\sqrt{5}$$

Multiply -9 and 3 to get -27.

$$9\sqrt{21}-27\sqrt{5}$$