When we divide two surds, we may or may not get a rational number.
When we divide two surds, we may or may not get a rational number.
The correct option is A True
Let us take two examples,
Example 1 3√3÷4√3
The value √3 is common to both terms and gets cancelled and we are left with the value of 34 which is a rational number since it can be represented in the form of pq where p and q are integers and q≠0
Example 2 5√5÷3√3
When we try dividing 5√5 by 3√3 we see that there are no common factors and we can’t divide it, even if we rationalize the denominator we will still get an irrational number
When we take both cases into consideration, we realize that in one case on dividing two irrational numbers we get a rational number whereas in the second case we find that we get an irrational number. This means that when we divide two irrational numbers, the number formed may or may not be a rational number.
True
Let us take two examples,
Example 1 3√3÷4√3
The value √3 is common to both terms and gets cancelled and we are left with the value of 34 which is a rational number since it can be represented in the form of pq where p and q are integers and q≠0
Example 2 5√5÷3√3
When we try dividing 5√5 by 3√3 we see that there are no common factors and we can’t divide it, even if we rationalize the denominator we will still get an irrational number
When we take both cases into consideration, we realize that in one case on dividing two irrational numbers we get a rational number whereas in the second case we find that we get an irrational number. This means that when we divide two irrational numbers, the number formed may or may not be a rational number.
