Which of the following is not irrational? (a) (3+sqrt(7)) (b) (3-sqrt(7)) (c) (3+sqrt(7))(3-sqrt(7)) (d) 3sqrt(7)
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Answer:
Correct answer is option (c); . It is a rational number and it is not irrational.
Explanation:
- The real numbers which can be represented in the form of ratio of two integers, as , where 'q' is not equal to zero are called rational numbers.
- The real numbers which cannot be expressed in the form of ratio of two integers are called as irrational numbers.
Step 1:
Consider option (a);
- We want to check wheather the number is rational number or irrational number.
- If we assume that is a rational number. So that we can write = , where p and q are coprime integers and q is not equal to 0.
if = , then =
⇒ =
- Since p and q are integers then, will be a rational number. So will be a rational number. But, this contradicts the fact that the number is an irrational one. This contradiction arises because of our wrong asssemption, i.e., is a rational number. Hence, our assemption is wrong and the number is an irrational number.
Similarly, consider option (b);
- We want to check wheather the number is rational number or irrational number.
- By following the same steps as earlier we can write;
= and =
- Since, the number is an irrational one, the number is an irrational number.
Step 2:
Consider option (c);
- We want to check wheather the number is rational number or irrational number.
- First we want to simplify the number by using the identity;
(a+b) (a-b) = , and then want to check whether the number is rational or not.
- By using the identity;
= -
⇒ 9 - 7
⇒ 2
- The number 2 can be written in the form of . That is .
- Hence the number is a rational number and it is not irrational.
Step 3:
Consider option (d);
- We want to check wheather the number is rational number or irrational number.
- Consider that the number is rational, then
=
- Rearranging the equation, we get; = .
- Since 3, p, q are integers it can be written in format and hence the number will be rational since is rational.
But in actual case the number is an irrational number. That is our assemption is contradiction to the real fact.
- Since is irrational, also the number is an irrational number.
- Therefore, the answer is option (c); . It is a rational number and it is not irrational.
To know more, go through the links;
https://brainly.in/question/39249959
https://brainly.in/question/33551114
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