Solve (5sqrt{2}-sqrt{3})5sqrt{2}+sqrt{12})

$$(5 \sqrt{ 2 } - \sqrt{ 3 } )5 \sqrt{ 2 } + \sqrt{ 12 } )$$

Evaluate

$$2\sqrt{3}+50-5\sqrt{6}\approx 41.216652901$$

Solution Steps

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

$$\left(25\sqrt{2}-5\sqrt{3}\right)\sqrt{2}+\sqrt{12}$$

Use the distributive property to multiply 25\sqrt{2}-5\sqrt{3} by \sqrt{2}.

$$25\left(\sqrt{2}\right)^{2}-5\sqrt{3}\sqrt{2}+\sqrt{12}$$

The square of \sqrt{2} is 2.

$$25\times 2-5\sqrt{3}\sqrt{2}+\sqrt{12}$$

Multiply 25 and 2 to get 50.

$$50-5\sqrt{3}\sqrt{2}+\sqrt{12}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$50-5\sqrt{6}+\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$50-5\sqrt{6}+2\sqrt{3}$$