Solve sqrt{15}(2sqrt{5}+sqrt{3})-2sqrt{75}=

$$\sqrt { 15 } ( 2 \sqrt { 5 } + \sqrt { 3 } ) - 2 \sqrt { 75 } =$$

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

Solution Steps

Use the distributive property to multiply \sqrt{15} by 2\sqrt{5}+\sqrt{3}.

$$2\sqrt{15}\sqrt{5}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

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}.

$$2\sqrt{5}\sqrt{3}\sqrt{5}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

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

$$2\times 5\sqrt{3}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}+\sqrt{15}\sqrt{3}-2\sqrt{75}$$

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}.

$$10\sqrt{3}+\sqrt{3}\sqrt{5}\sqrt{3}-2\sqrt{75}$$

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

$$10\sqrt{3}+3\sqrt{5}-2\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$10\sqrt{3}+3\sqrt{5}-2\times 5\sqrt{3}$$

Multiply -2 and 5 to get -10.

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

Combine 10\sqrt{3} and -10\sqrt{3} to get 0.

$$3\sqrt{5}$$