Solve 5sqrt{10}(2sqrt{6}-7sqrt{5})

$$5 \sqrt { 10 } ( 2 \sqrt { 6 } - 7 \sqrt { 5 } )$$

Evaluate

$$20\sqrt{15}-175\sqrt{2}\approx -170.027706491$$

Solution Steps

Use the distributive property to multiply 5\sqrt{10} by 2\sqrt{6}-7\sqrt{5}.

$$10\sqrt{10}\sqrt{6}-35\sqrt{10}\sqrt{5}$$

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

$$10\sqrt{60}-35\sqrt{10}\sqrt{5}$$

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$10\sqrt{60}-35\sqrt{5}\sqrt{2}\sqrt{5}$$

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

$$10\sqrt{60}-35\times 5\sqrt{2}$$

Multiply -35 and 5 to get -175.

$$10\sqrt{60}-175\sqrt{2}$$

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}.

$$10\times 2\sqrt{15}-175\sqrt{2}$$

Multiply 10 and 2 to get 20.

$$20\sqrt{15}-175\sqrt{2}$$