Question

Classify the below expression as rational or irrational:2 root 2 ÷ 4 root 2

Answer 1

Rational number

STEP - BY - STEP EXPLANATION

What to do?

Determine whether the given expression is a rational or irrational.

Given:

`2√(2)/4√(2)`

To solve the given expression, we will follow the steps below:

Step 1

Re-write the expression in a fraction format.

`(2√(2))/(4√(2))`

Step 2

Cancel-out the root 2 since it is common on the numerator and denominator.

`=\frac{2\cancel{√(2)}}{4\cancel{√(2)}}`

Step 3

Reduce the fraction.

`=(1)/(2)`

Step 4

Determine if it is rational or irrational.

A rational number is a number that can be represented in the form a/b where a, b are integers and b is not equal to zero.

Observe that 1/2 is of form a/b.

Hence, it is a rational number.