Question

How do you simplify \[\sqrt 8 + \sqrt 2 \]?

Answer 1

Hint: In the given question, we have been given two numbers inside the square root bracket. We have to simplify them by finding their sum. We are first going to simplify the square root bracket – taking out the equal number pairs as a single number. Then we are going to solve them by adding them.

Complete step by step answer:
The given expression in algebraic expression is:
\[\sqrt 8 + \sqrt 2 \]
First, we will solve the square root brackets:
\[\sqrt 8 = \sqrt {2 \times 4} = \sqrt {2 \times {{\left( 2 \right)}^2}} = 2\sqrt 2 \]
\[\sqrt 2 = 1\sqrt 2 \]
So, \[\sqrt 8 + \sqrt 2 = 2\sqrt 2 + 1\sqrt 2 = 3\sqrt 2 \]

Hence, the value of \[\sqrt 8 + \sqrt 2 \] is \[3\sqrt 2 \].

Additional Information:
We can add two square roots only if they have the same number inside the square root bracket. The same thing applies to the operation of subtraction. But, in the case of multiplication or division, we can multiply or divide any two square root numbers and they are going to be treated as a single number.

Note:
In the given question, we were given two numbers inside two different square root brackets. We had to simplify their sum. We did that by first simplifying the square root bracket – taking out the equal number pairs as a single number, and then solving them by adding them.