Solve sqrt{15}(sqrt{3}-sqrt{5}+sqrt{6})

$$\sqrt { 15 } ( \sqrt { 3 } - \sqrt { 5 } + \sqrt { 6 } )$$

Evaluate

$$3\sqrt{5}+3\sqrt{10}-5\sqrt{3}\approx 7.534782875$$

Solution Steps

Use the distributive property to multiply \sqrt{15} by \sqrt{3}-\sqrt{5}+\sqrt{6}.

$$\sqrt{15}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{6}$$

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}.

$$\sqrt{3}\sqrt{5}\sqrt{3}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{6}$$

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

$$3\sqrt{5}-\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{6}$$

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

$$3\sqrt{5}-\sqrt{5}\sqrt{3}\sqrt{5}+\sqrt{15}\sqrt{6}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$3\sqrt{5}-5\sqrt{3}+\sqrt{15}\sqrt{6}$$

To multiply \sqrt{15} and \sqrt{6}, multiply the numbers under the square root.

$$3\sqrt{5}-5\sqrt{3}+\sqrt{90}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$3\sqrt{5}-5\sqrt{3}+3\sqrt{10}$$