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

Answer:

Did you copy this down correctly?

Step-by-step explanation:

b = .125 which is rational

a is irrational because the square root of a prime number is irrational.

If c = 225....

then adding 2 rational numbers = rational sum

But adding (or multiplying) an irrational number to a rational number = irrational number.

Answer 2

The a +b is irrational because  the sum of rational and irrational number is 'a' irrational number and  b + c is rational because adding two rational number is rational, as c is the rational number.

What is an irrational number?

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

We have:

20b = 2.5

b = 0.125

a = √20

c = 225

= a + b

= √20 + 0.125

Here 'a' is irrational because the square root of a prime number is irrational.

And b is the rational number

The sum of rational and irrational number is 'a' irrational number.

= b + c

= 0.125 + 225

b = 0.125 which is rational

Adding to rational number is rational, as c is the rational number.

Thus, the a +b is irrational because  the sum of rational and irrational number is 'a' irrational number and  b + c is rational because adding two rational number is rational, as c is the rational number.

Learn more about the irrational number here:

brainly.com/question/17450097

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