We start with the expression at the left of the equation.
We can combine the terms as:
![\begin{gathered} \frac{2+\sqrt[]{3}}{\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}}}-\frac{2-\sqrt[]{3}}{\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}}} \\ \frac{2+\sqrt[]{3}}{\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}}}\cdot\frac{(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})}-\frac{2-\sqrt[]{3}}{\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}}}\cdot\frac{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})} \\ \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})-(2-\sqrt[]{3})\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D-%5Cfrac%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%20%5C%5C%20%5Cfrac%7B2%2B%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%5Ccdot%5Cfrac%7B%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D-%5Cfrac%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7B%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%5Ccdot%5Cfrac%7B%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%20%5C%5C%20%5Cfrac%7B%282%2B%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29-%282-%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%20%5Cend%7Bgathered%7D)
We can now apply the distributive property for the both the numerator and denominator. We can see also that the denominator is the expansion of the difference of squares:
![\begin{gathered} \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})-(2-\sqrt[]{3})\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{(\sqrt[]{2})^2-(\sqrt[]{2-\sqrt[]{3}}))^2} \\ \frac{(2+\sqrt[]{3})\cdot(\sqrt[]{2}-\sqrt[]{2-\sqrt[]{3}})+(\sqrt[]{3}-2)\cdot(\sqrt[]{2}+\sqrt[]{2-\sqrt[]{3}})}{2^{}-(2-\sqrt[]{3})^{}} \\ \frac{\sqrt[]{2}\cdot(2+\sqrt[]{3})-\sqrt[]{2-\sqrt[]{3}}\cdot(2+\sqrt[]{3})+\sqrt[]{2}\cdot(\sqrt[]{3}-2)+\sqrt[]{2-\sqrt[]{3}}\cdot(\sqrt[]{3}-2)}{2-2+\sqrt[]{3}} \\ \frac{\sqrt[]{2}(2+\sqrt[]{3}+\sqrt[]{3}-2)+\sqrt[]{2-\sqrt[]{3}}(-2-\sqrt[]{3}+\sqrt[]{3}-2)}{\sqrt[]{3}} \\ \frac{\sqrt[]{2}(2\sqrt[]{3})+\sqrt[]{2-\sqrt[]{3}}(-4)}{\sqrt[]{3}} \\ 2\sqrt[]{2}-4\frac{\sqrt[]{2-\sqrt[]{3}}}{\sqrt[]{3}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B%282%2B%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29-%282-%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B%28%5Csqrt%5B%5D%7B2%7D%29%5E2-%28%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%29%5E2%7D%20%5C%5C%20%5Cfrac%7B%282%2B%5Csqrt%5B%5D%7B3%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%2B%28%5Csqrt%5B%5D%7B3%7D-2%29%5Ccdot%28%5Csqrt%5B%5D%7B2%7D%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%29%7D%7B2%5E%7B%7D-%282-%5Csqrt%5B%5D%7B3%7D%29%5E%7B%7D%7D%20%5C%5C%20%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%5Ccdot%282%2B%5Csqrt%5B%5D%7B3%7D%29-%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%282%2B%5Csqrt%5B%5D%7B3%7D%29%2B%5Csqrt%5B%5D%7B2%7D%5Ccdot%28%5Csqrt%5B%5D%7B3%7D-2%29%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%5Ccdot%28%5Csqrt%5B%5D%7B3%7D-2%29%7D%7B2-2%2B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%282%2B%5Csqrt%5B%5D%7B3%7D%2B%5Csqrt%5B%5D%7B3%7D-2%29%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%28-2-%5Csqrt%5B%5D%7B3%7D%2B%5Csqrt%5B%5D%7B3%7D-2%29%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%282%5Csqrt%5B%5D%7B3%7D%29%2B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%28-4%29%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%202%5Csqrt%5B%5D%7B2%7D-4%5Cfrac%7B%5Csqrt%5B%5D%7B2-%5Csqrt%5B%5D%7B3%7D%7D%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5Cend%7Bgathered%7D)
We then can continue rearranging this as:
Answer:
Given the equation, the radius of the circle is 7.
Step-by-step explanation:
We are given the equation, x² + y² = 49.
In order to find the radius, we have to calculate the square root of 49. This is because the original form of the equation is x² + y² = r².
So, the radius of the circle is 7.
Answer:
The probability that 2 certain people will serve on that committee is 11.11%.
Step-by-step explanation:
Since to make a committee 4 men are chosen out of 6 candidates, to determine what is the probability that 2 certain people will serve on that committee the following calculation must be performed:
4/6 = 2/3
1/3 x 1/3 = X
0.333 x 0.333 = X
0.1111 = X
Therefore, the probability that 2 certain people will serve on that committee is 11.11%.
Answer:
A = $15,696.72
Step-by-step explanation:
Use the compound amount formula: A = P(1 + r/n)^(nt). Here the number of compounding periods is nt, or (12 per year)(5 years) = 60.
Our formula becomes A = $11,499(1 + 0.062/12)^60, which works out to:
A = $11,499(1 + 0.0052)^60, or
A = $15,696.72
The monthly payment is $15,696.72/60, or $261.61.
Answer:
5
Step-by-step explanation:
