Question

A teacher wrote the following set of numbers on

the board:
20 b = 2.5
Explain why a +b is irrational, but b + c is rational.
a= V20
C= 225

Answer 1

Step-by-step explanation:

From the equation 20b = 2.5, we can solve for b:

20b = 2.5b = 2.5/20b = 1/8

Therefore, b is rational.

a = √20 is irrational because 20 is not a perfect square.

c = 225 is a perfect square, specifically 15^2. Therefore, c is rational.

Now, we can evaluate a + b and b + c:

a + b = √20 + 1/8

Since a is irrational and b is rational, their sum (a + b) is irrational.b + c = 1/8 + 225

Since b and c are both rational, their sum (b + c) is rational.So, the reason why a + b is irrational but b + c is rational is because one of the terms in the sum is irrational in the former case and both terms are rational in the latter case.