Question

Every surb is an irrational , but every irrational need not be a surb . Justify your answer. ​

Answer 1

Hint: We recall the definition of rational, irrational number and surds. We observe that every irrational number cannot be expressed.

Complete step by step answer:

We call a number irrational when cannot express that number in the form pq for example √2,3√4.

There are also transcendental numbers like π,e also cannot be expressed in the form of p√n=n1p and hence are not surds but they are irrationals. This is why every surd is irrational, but every irrational need not be a surd.

Note: We note that the other name of surd is nth root since all surds are solutions to the polynomial equation xn=a where a is any irrational number while those numbers which are solutions to polynomial equation like axn+axn−1+....+a0=0 are called algebraic numbers and which cannot be solutions are called transcendental numbers.