Find the square root of 12-22square root 2
looks like you want
√(12 - 22√2)
looks like you are trying to take the square root of a negative.
Have you heard of DeMoivre's theorem?
Could you help me with the problem?
I was trying to establish at what level of math you are working.
That is why I asked about DeMoivre's theorem.
As a short answer:
√(12 - 22√2) = √(22√2 - 12) i
= appr 19.11 i
To find the square root of 12 - 22√2, we can break it down into two parts.
First, let's calculate the value of -22√2, which is an irrational number. In order to simplify this, we need to simplify the square root of 2. We know that the square root of 2 cannot be simplified further, as it is an irrational number.
Now, let's calculate the square root of 12 - 22√2:
√(12 - 22√2)
To simplify this expression, we can use a technique called "rationalizing the denominator." We do this by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √2 is -√2.
√(12 - 22√2) * (-√2) / (-√2)
= (-√2)(12 - 22√2) / (-2)
= (-12√2 + 22 * 2) / (-2)
= (-12√2 + 44) / (-2)
= -22 + 6√2
So, the square root of 12 - 22√2 is -22 + 6√2.