x Show that 4 V2 is an irrational number.
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Step-by-step explanation:
Let 4√2 be a rational number.
A rational number can be written in the form of p/q.
4√2 = p/q
p = 4√2q
Squaring on both sides,
p²=16(2)q²
2 divides p² then 2 also divides p.
So, p is a multiple of 2.
p = 2a (a is any integer)
Put p=2a in p²=32q²
(2a)² = 32q²
4a² = 32q²
2a² = 16q²
2 divides q² then 2 also divides q.
Therefore,q is also a multiple of 2.
So, q = 2b
=> Both p and q have 2 as a common factor.
But this contradicts the fact that p and q are co primes.
So our supposition is false.
Therefore, 4√2 is an irrational number.
Hence proved.
Hope it helps
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