Prove that √3 + √5 is irrational
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Heya !!!
Let suppose that ( ✓3 + ✓5) is rational Number.
Let (✓3 + ✓5) = A , where A is rational Number.
Then , ✓3 = ( A - ✓5) -------(1)
On squaring both sides of (1) we get,
3 = A² +5 - 2A ✓5 = 3A✓5 = A²+1
Therefore,
✓5 = A²+1/3A --------(2)
This is impossible , as the right hand side is rational , while ✓5 is irrational.
Our SUPPOSITION is wrong that ✓3 + ✓5 is rational.
Hence,
✓3 + ✓5 is irrational Number.
HOPE IT WILL HELP YOU....... :-)
Let suppose that ( ✓3 + ✓5) is rational Number.
Let (✓3 + ✓5) = A , where A is rational Number.
Then , ✓3 = ( A - ✓5) -------(1)
On squaring both sides of (1) we get,
3 = A² +5 - 2A ✓5 = 3A✓5 = A²+1
Therefore,
✓5 = A²+1/3A --------(2)
This is impossible , as the right hand side is rational , while ✓5 is irrational.
Our SUPPOSITION is wrong that ✓3 + ✓5 is rational.
Hence,
✓3 + ✓5 is irrational Number.
HOPE IT WILL HELP YOU....... :-)
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