Question

Given the two expressions shown below:

A: square root of 3 plus square root of 2

B: square root of 3 plus square root of 6

Which statement best describes the two expressions?



A. Both are rational.


B. Both are irrational.


C. A is rational, but B is irrational.


D. A is irrational, but B is rational.

Answer 1

Plug em into a calculator and they are both irrational

Answer 2

B. Both are irrational

Explanation:

We know that,

Rational numbers are the numbers that can be written in the form
`(p)/(q)`, where q≠0.

Irrational numbers are the numbers which are not rational i.e. cannot be written in the form
`(p)/(q)`, where q≠0.

According to our question,

A =
`√(3) +√(2)`, this cannot be simplifies further and can never be written as
`(p)/(q)`.

Similarly, B =
`√(3) +√(6)`, cannot be simplified further into
`(p)/(q)` form.

Hence, both the numbers in A and B are irrational numbers.