Show that 5√3 is an irrational number.
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irrational
Step-by-step explanation:
Let suppose 5−3–√ as a rational number
As we know that 5−3–√ is an rational number then 5−3–√ = pq where p and q are coprime numbers and q is not equal to zero here Coprime numbers can be defined as the number or integers which have only ‘1’ as the highest common factor
So, we have 5−3–√ = pq
Now Rearranging terms in the above equation i.e. 5−3–√=pq , we get
−3–√=pq−5
−3–√=p−5qq
3–√=5q−pq
Now, 5q−pq is clearly a rational number as both p and q are integers.
So, by the above statement we can say that 3–√ is a rational number
Thus, our assumption is incorrect
Therefore, the number 5−3–√ is irrational.
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