hi in quants prepswift questions we are asked if root(7) is a rational or irrational number
do we memorise that root(7) is irrational or is that something we can calculate?
in gre calculator we get only up to 8 digits so what if we get some number that repeats after 8 digits?
if a number has a pattern that repeats then it is a rational number right
You mean \sqrt{n}, where n is an integer? That either is an integer (eg when n = 9) or is irrational. The concept of “a number has a pattern that repeats then it is a rational number” is for non-integers, such as \frac{1}{7}.
irrational means it cannot be expressed in fractional form right? if so how do we know the value of a √n cannot be expressed in fractions?
like √4 is 2 now this is rational since we can express 2 as 2/1
now for a number like √7 how can we conclude it is irrational.
Because unless we get a decimal value that is not repeating or non terminating we cannot say it is irrational right?
You cannot write \sqrt{7} in the form p/q where p and q are integers.
yeah correct my question is how do we determine if a root can be written in p/q do we check the root value in calculator and see if the value we get can be fractionalized or is there a general conclusion like if the integer is not a perfect square then the square root of the integer will be irrational.
This is true.