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

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

Evaluate

$$19\sqrt{2}\approx 26.870057685$$

Solution Steps

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

$$25\sqrt{2}-10\sqrt{3}+5\sqrt{6}\sqrt{2}-2\sqrt{6}\sqrt{3}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$25\sqrt{2}-10\sqrt{3}+5\sqrt{2}\sqrt{3}\sqrt{2}-2\sqrt{6}\sqrt{3}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$25\sqrt{2}-10\sqrt{3}+5\times 2\sqrt{3}-2\sqrt{6}\sqrt{3}$$

Multiply 5 and 2 to get 10.

$$25\sqrt{2}-10\sqrt{3}+10\sqrt{3}-2\sqrt{6}\sqrt{3}$$

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

$$25\sqrt{2}-2\sqrt{6}\sqrt{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$25\sqrt{2}-2\sqrt{3}\sqrt{2}\sqrt{3}$$

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

$$25\sqrt{2}-2\times 3\sqrt{2}$$

Multiply -2 and 3 to get -6.

$$25\sqrt{2}-6\sqrt{2}$$

Combine 25\sqrt{2} and -6\sqrt{2} to get 19\sqrt{2}.

$$19\sqrt{2}$$