Question

prove that the following numbers are irrational √3+√5​

Answer 1

Let us suppose that √3-√5 is rational and is equal to a/b where a and b are co-prime.

Since a, b, 8,2 are rational numbers a^2–8b^2/-b^2 should also be rational.

And √15 should also be rational but this contradicts the fact that √15 is irrational.

Therefore our supposition was wrong and √3-√5 is irrational

Answer 2

let be √3+√5 is irrational number is r say

then √3+√5 =r

on squaring both sides,

(√3+√5)²=r²

3+2√15+5=r

8+2√15=r²

2√15=r²-8

√15=(r²-8)/2

now (r²-8)/2 is a rational number and √15 is a irrational number.

since,a rational number cannot be equal to a irrational number . our assumption is that √3+√5 is wrong.

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