Question

Is the following expression a rational or irrational number?ii) (2 root 2 + 3 root 2) + (3 root 2 - 5 root 2)

Answer 1

Recall that:

`a√(b)+c√(b)=(a+c)√(b).`

Therefore:

`\begin{gathered} 2√(2)+3√(2)=(2+3)√(2)=5√(2), \\ 3√(2)-5√(2)=(3-5)√(2)=-2√(2). \end{gathered}`

Substituting the above results in the given expression we get:

`5√(2)-2√(2).`

Then:

`(2√(2)+3√(2))+(3√(2)-5√(2))=3√(2).`

Now, we know that

`√(2)`

is an irrational number, then

`3√(2)`

is also an irrational number.

Answer: The given expression is an irrational number.