Math, asked by Arzoo12345, 1 year ago

prove that under root 5 minus under root 2 is irrational

Answers

Answered by broke
1
The answer is in photograph
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Arzoo12345: thanks
Answered by Anonymous
2
Hey there !!
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Let √5 – √2 be rational.

√5 – √2 = a / b where a and b are co-prime and (b≠0)

Squaring both sides,
(√5 – √2)² = ( a / b )²

=> 7 – 2√10 = a²/b²

=> 7 – (a²/b²) = 2√10

=> √10 = [ 7 – (a²/b²) ] / 2

Since a and b are integers so, [ 7 – (a²/b²) ] / 2 is a rational number.

So, √10 is also a rational number.

But this contradicts that the fact that √10 is irrational. Our consumption is false.

So, we conclude that √5 – √2 is an irrational number.
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Anonymous: Thanks ☺❤
Arzoo12345: ur welcome nd thank u 2 for helping...
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