If the square root of a number is irrational, it is its own conjugate.
sqrt(13)*sqrt(13) = 13 and you no longer have an irrational!
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a+ square root of b has a conjugate a- square root of b and this is used rationalize the denominator when it contains a square root. If we want to multiply 5 x square root of 10 by something to get rid of the radical you can multiply it by square root of 10. But if we look at 5x( square root of 10 as ) 0+ 5x square root of 10 then the conjugate would be -5x square root of 10
The square root of 169 = ± 13
13, is not the square root of 156, but the best i can give you is that 13 is the square root of 169 and 14 is the square root of 196.
This is related to the technique used to eliminate square roots from the denominator. If, for example, the denominator is 4 + root(3), you multiply both numerator and denominator by 4 - root(3). In this case, "4 - root(3)" is said to be the "conjugate" of "4 + root(3)". When doing this, there will be no more square roots in the denominator - but of course, you'll instead have a square root in the numerator.
169. 13 x 13 = 169. square root of 169 = 13.