Question

Prove that 5 - √2 is irrational number.
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Answer 1

Answer:-

Let us assume 5-√2 is a rational no.

So , according to the definition of rational no.

5-√2 = a/b where a and b are co-prime and b is not equal to zero.

Now shifting 5 to other side we get

-√2=a/b -5

√2= - a/b+5

√2=(-a+5b)/b

Since a , b and 5 are rational so their addition as well as division would be rational ..

But √2 is irrational and √2 cannot be equal to a rational no.

This contradicts the fact that √ 2 is irrational

This contradiction arises when we 5-√2 as rational

So, 5-√2 is irrational

( We can prove √ 2 is irrational )

Answer 2

Answer:

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Step-by-step explanation:

Let us assume that 5–√2 is a rational number and it's simplest form is p/q.

then, p and q are integers having no common factor other than 1 and q ≠ 0.

so,

5–√2 = p/q

√2 = 5–p/q

√2 = (5q–p) / 5

thus, p and q are integers and q ≠ 0.

so, (5q–p) /5 is a rational number.

therefore, √2 is also a rational number.

But, this contradicts the fact that √2 is irrational.

The contradiction arises by assuming 5–√2 is rational.

so, our assumption is wrong.

Hence, 5–√2 is irrational.

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