Question

The number (√5+2)/(√5-2)

is:
(a) a rational number
(b) an irrational number
(c) an integer
(d) a natural number

Answer 1

b: irrational

Explanation:

(√5+2)

-------------- is given.

(√5 - 2)

If we multiply numerator and denominator by (√5+2), we succeed in removing the square root symbol from the denominator:

(√5+2)(√5+2)

---------------------

(√5+2)(√5- 2)

and the denominator becomes 5 - 2, or 3. The denominator is now rational, but the numerator still involves the square root symbol, so overall the given number is irrational.