Solve (4-5sqrt{6})(3+5sqrt{10})

$$( 4 - 5 \sqrt { 6 } ) ( 3 + 5 \sqrt { 10 } )$$

Evaluate

$$20\sqrt{10}+12-15\sqrt{6}-50\sqrt{15}\approx -155.145960249$$

Solution Steps

Apply the distributive property by multiplying each term of 4-5\sqrt{6} by each term of 3+5\sqrt{10}.

$$12+20\sqrt{10}-15\sqrt{6}-25\sqrt{6}\sqrt{10}$$

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

$$12+20\sqrt{10}-15\sqrt{6}-25\sqrt{60}$$

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}.

$$12+20\sqrt{10}-15\sqrt{6}-25\times 2\sqrt{15}$$

Multiply -25 and 2 to get -50.

$$12+20\sqrt{10}-15\sqrt{6}-50\sqrt{15}$$