Solve (sqrt{10}+2)(3sqrt{15}-5sqrt{6})

$$( \sqrt { 10 } + 2 ) ( 3 \sqrt { 15 } - 5 \sqrt { 6 } )$$

Evaluate

$$5\sqrt{6}-4\sqrt{15}\approx -3.244484671$$

Solution Steps

Apply the distributive property by multiplying each term of \sqrt{10}+2 by each term of 3\sqrt{15}-5\sqrt{6}.

$$3\sqrt{10}\sqrt{15}-5\sqrt{10}\sqrt{6}+6\sqrt{15}-10\sqrt{6}$$

To multiply \sqrt{10} and \sqrt{15}, multiply the numbers under the square root.

$$3\sqrt{150}-5\sqrt{10}\sqrt{6}+6\sqrt{15}-10\sqrt{6}$$

To multiply \sqrt{10} and \sqrt{6}, multiply the numbers under the square root.

$$3\sqrt{150}-5\sqrt{60}+6\sqrt{15}-10\sqrt{6}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$3\times 5\sqrt{6}-5\sqrt{60}+6\sqrt{15}-10\sqrt{6}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{6}-5\sqrt{60}+6\sqrt{15}-10\sqrt{6}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$15\sqrt{6}-5\times 2\sqrt{15}+6\sqrt{15}-10\sqrt{6}$$

Multiply -5 and 2 to get -10.

$$15\sqrt{6}-10\sqrt{15}+6\sqrt{15}-10\sqrt{6}$$

Combine -10\sqrt{15} and 6\sqrt{15} to get -4\sqrt{15}.

$$15\sqrt{6}-4\sqrt{15}-10\sqrt{6}$$

Combine 15\sqrt{6} and -10\sqrt{6} to get 5\sqrt{6}.

$$5\sqrt{6}-4\sqrt{15}$$