Question

Find the value of
$$2\sqrt 2 + 3\sqrt 2 $$

Answer 1

Hint: We have irrational numbers given in the above question. Irrational numbers are those numbers which are real number but not rational numbers. We have a common irrational number in the given question. Therefore, we can add only the given rational numbers and keep the irrational numbers as it is. Irrational numbers cannot be added or subtracted directly. Since we do not need their values, we will keep them as they are.

Complete step-by-step answer:
Let us consider the given problem,
$$2\sqrt 2 + 3\sqrt 2 $$
Now, we have $$\sqrt 2 $$ common in both the terms.
Therefore, we can take that as a common term.
We get,
$$ \Rightarrow 2\sqrt 2 + 3\sqrt 2 = \sqrt 2 \left( {2 + 3} \right)$$
Now, since there are two real numbers in the round brackets, we add them.
$$ \Rightarrow 2\sqrt 2 + 3\sqrt 2 = \sqrt 2 \left( 5 \right)$$
We always express the real number first and then we write the irrational part.
Therefore, we get
$$2\sqrt 2 + 3\sqrt 2 = 5\sqrt 2 $$
So, the final answer for the given question is $$5\sqrt 2 $$.

Additional Information:
An irrational number is a number which cannot be expressed as a simple fraction. It cannot be expressed as a rational number as well. They have decimal expansions which are neither periodic nor terminal. That means, the decimals do not end, nor do they repeat. The examples for irrational numbers are $$\sqrt 2 ,\sqrt 3 ,\sqrt 5 $$, and so on.

Note: The given question is very simple. We are only supposed to add the given set of irrational numbers. Note that an irrational number along with a rational number can be considered as two different terms while adding or subtracting. Therefore, make sure that you group the rational terms and keep the irrational term. Only if they have given a particular value for the irrational number, can you substitute.