Question

prove that 3-2 root 5 is irrational number​

Answer 1

Answer:

Step-by-step explanation:

3 - 2√5 = a/ b

-2√5 =a/b -3

√5 =a-3b/-2b

√5 is rational.

This contradicta the fact that √5 is irrational.

So our supposition is incorrect.

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Answer 2

so this is from chapter real numbers

let us suppose that 3-2√ 5 is a rational number

that means

3-2√ 5 = p/q where p and q are integers and co prime

-2√ 5 = p/q-3

-2√ 5 = p-3q/q

√ 5 = p-3q/-2q  (cross multiplying)

but √ 5 is an irrational number

=> that p-3q/-2q is also irrational

this contradicts our assumption that 3-2√ 5 is rational

=> 3-2√ 5 is irrational

hence.proved.

Hope this helps!