express the following fraction in the form of m + (n)^1/2. the fraction is ((3*(5)^1/2)^2 - 7)/(3 + 7*(5)^1/2). where m,n are real numbers.

first of all you would see that at the bottom of the fraction it is not an integer so first of all you would need to rationalise the denominator. the denominator is the bit at the bottom of the fraction. You would do this by multiplying both the top and bottom of the fraction but the number which is the conjugate to that of the number on the denominator, in this case it would be (3 - 7*(5)^1/2). from this you would get an integer on the bottom on the fraction, which here would be 354 . from here you would need to multiple the numerator by the same thing you did on the denominator and then you are able to get a number in the form m + n(5)1/2, which in this case is (114 - 266*(5)^1/2)/354