Show that5+2√7 is an irrational number where√7 is a irrational number
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Given:
- We have been given a number 5 + 2√7.
- It is also given that √7 is irrational.
To Show:
- We need to show that 5 + 2√7 is an irrational number.
Solution:
Let us assume that 5 + 2√7 is an rational number.
Therefore, 5 + 2√7 can be written in the form of p/q where p and q are integers and q is not equal to zero.
=> 5 + 2√7 = p/q
=> 2√7 = p/q - q
=> √7 = p - 5q/2q
Since, p and q are integers, therefore √7 is rational. But this contradicts the fact that √7 is irrational. Therefore, our assumption was wrong.
Hence, 5 + 2√7 is an irrational number.
Answered by
1
- We have been given a number 5 + 2√7
- It is also given that root 7 is irrational.
we now to that 5 + 2√7 is an irrational number.
- Let we assume that 5 + 2√7 is an rational number.
Therefore,
5 + 2√7 can in the form of p/q where p and q are integer and q is is not equal to zero.
5 + 2√7 = p/q
2√7 = p/q - p
√7 = p - 5q/2q
since, p and q are integer therefore √7 is rational. but contradict, the fact that √7 is irrational. therefore, assumption was wrong.
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