Math, asked by Itzmemansi07, 1 month ago

Show that 5√3 is an irrational number.​

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Answered by mangeshub
0

Answer:

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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