Question

sqrt(12-6*sqrt(3))+sqrt(4-2*sprt(3)

Answer 1

4-2sqrt(3)=(sqrt(3)-1)^2

12-6sqrt(3)=(3-sqrt(3))^2

sqrt(3)-1+3-sqrt(3)=2

Answer 2

$\sqrt{12-6\sqrt{3}}+\sqrt{4-2\sqrt{3}}=\\\\\sqrt{9-6\sqrt{3}+3}+\sqrt{3-2\sqrt{3}+1}=\\\\\sqrt{3^2-2*3*\sqrt{3}+(\sqrt{3})^2}+\sqrt{(\sqrt{3})^2-2*\sqrt{3}*1+1^2}=\\\\\sqrt{(3-\sqrt{3})^2}+\sqrt{(\sqrt{3}-1)^2}=\\\\|3-\sqrt{3}|+|\sqrt{3}-1|=3-\sqrt{3}+\sqrt{3}-1=2$

Answer 3

To simplify the expression sqrt(12-6*sqrt(3)) + sqrt(4-2*sqrt(3)), we can follow these steps:

Step 1: Simplify the expressions inside the square roots:

sqrt(12-6*sqrt(3)) = sqrt(12) - sqrt(6*sqrt(3)) = sqrt(12) - sqrt(6) * sqrt(sqrt(3)) = sqrt(12) - sqrt(6) * sqrt(3^(1/2)) = sqrt(12) - sqrt(6) * sqrt(3)^(1/2) = sqrt(12) - sqrt(6) * sqrt(3) = sqrt(12) - sqrt(6) * sqrt(3) = 2 * sqrt(3) - sqrt(6)

sqrt(4-2*sqrt(3)) = sqrt(4) - sqrt(2*sqrt(3)) = sqrt(4) - sqrt(2) * sqrt(sqrt(3)) = sqrt(4) - sqrt(2) * sqrt(3^(1/2)) = sqrt(4) - sqrt(2) * sqrt(3)^(1/2) = sqrt(4) - sqrt(2) * sqrt(3) = 2 - sqrt(2) * sqrt(3)

Step 2: Substitute the simplified expressions back into the original expression:

sqrt(12-6*sqrt(3)) + sqrt(4-2*sqrt(3)) = (2 * sqrt(3) - sqrt(6)) + (2 - sqrt(2) * sqrt(3))

Step 3: Combine like terms:

= 2 * sqrt(3) - sqrt(6) + 2 - sqrt(2) * sqrt(3)

Step 4: Simplify further:

= 2 * sqrt(3) - sqrt(6) + 2 - sqrt(6)

Step 5: Combine like terms:

= 2 * sqrt(3) - sqrt(6) - sqrt(6) + 2

= 2 * sqrt(3) - 2 * sqrt(6) + 2

So the simplified form of sqrt(12-6*sqrt(3)) + sqrt(4-2*sqrt(3)) is 2 * sqrt(3) - 2 * sqrt(6) + 2.