Question

Prove that root3 +root5 is a irrational no

Answer 1

Let X be a rational no.= ✓3 +✓5
X squared = (✓3+ ✓5)squared
That is,
X squared= 3+5+2✓15
X2=8+2✓15
(X squared - 8)= 2✓15
As We Supposed X Is Rational So x squared must also be rational.
and as a rational - a rational must give a rational no.
so X2 minus 8 must be rational.
but we know that 2✓15 is Irrational.
So Our Supposition Was Wrong.
Thus ✓3 + ✓5 is Irrational.

Answer 2

Answer:

Step-by-step explanation:

firstly, let us assume it is rational,

√3+√5=a/b

√5=a/b-√3

√5=a-√3b/b

squaring both the sides,

we get,

5=(a-√3b)²/b²

then,

5b²=(a-√3b)²

5b²=a²-2√3ab+b²

5b²-b²=a²-2√3ab

4b²=a²-2√3ab

√3=4b²/a²-2ab

it is rational but √3 is not rational

∴this is irrational.