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Show that root2 + root3 is …

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Show that root2 + root3 is irrational...

Posted by Mahi ✌?? 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 10 months ago

Let √2 + √3 = (a/b) is a rational no.
On squaring both sides , we get
2 + 3 + 2√6 = (a²/b²)
So,5 + 2√6 = (a2/b2) a rational no.
So, 2√6 = (a²/b²) – 5
Since, 2√6 is an irrational no. and (a²/b²) – 5 is a rational no.
So, my contradiction is wrong.
So, (√2 + √3) is an irrational no.

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CBSE > Class 10 > Mathematics