Question

Show that 4√2 is an irrational numbers.​

Answer 1

Answer:

Let us assume that 4√2 is a rational number.

So, we can find co-prime integers ‘a’ and ‘b’ (b ≠ 0) such that

Since,

32 divides a2, so

32 divides ‘a’ as well.

So, we write a = 32c, where c is an integer.

∴ a2 = (32c)2 … [Squaring both the sides]

∴ 32b2 = 32 x 32c2 …[From(i)]

∴ b2 = 32c2

∴ c2 = b2/32

Since, 32 divides b2,

so 32 divides ‘b’.

∴ 32 divides both a and b.

a and b have at least 32 as a common factor. But this contradicts the fact that a and b have no common factor other than 1.

∴ Our assumption that 4√2 is a rational number is wrong.

∴ 4√2 is an irrational number

Step-by-step explanation:

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