Solve 9-sqrt{3}(sqrt{5}-sqrt{30})

$$9 - \sqrt { 3 } ( \sqrt { 5 } - \sqrt { 30 } )$$

Evaluate

$$3\sqrt{10}+9-\sqrt{15}\approx 14.613849634$$

Solution Steps

Use the distributive property to multiply \sqrt{3} by \sqrt{5}-\sqrt{30}.

$$9-\left(\sqrt{3}\sqrt{5}-\sqrt{3}\sqrt{30}\right)$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$9-\left(\sqrt{15}-\sqrt{3}\sqrt{30}\right)$$

Factor 30=3\times 10. Rewrite the square root of the product \sqrt{3\times 10} as the product of square roots \sqrt{3}\sqrt{10}.

$$9-\left(\sqrt{15}-\sqrt{3}\sqrt{3}\sqrt{10}\right)$$

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

$$9-\left(\sqrt{15}-3\sqrt{10}\right)$$

To find the opposite of \sqrt{15}-3\sqrt{10}, find the opposite of each term.

$$9-\sqrt{15}-\left(-3\sqrt{10}\right)$$

The opposite of -3\sqrt{10} is 3\sqrt{10}.

$$9-\sqrt{15}+3\sqrt{10}$$