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Question

1+3 is a real rational number.

A
True
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B
False
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Solution

The correct option is B False
Let us assume that the square root of the prime number p is rational.
Hence we can write p=ab where a and b are coprime numbers.
Then p=a2b2 and so pb2=a2.
Hence, p divides a2,so p divides a.
Substitute a by pk. Find out that p divides b.
Hence, this is a contradiction as they should be relatively prime i.e., H.C.F.(a,b)=1.

3 is irrational.
1+3 is an irrational number.

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