Question

NOTES
Date
Home Assignment
show that every
23. prove that 5+2√3
is irritational number​

Answer 1

Answer:

let 5+2√3 is a rational no. in the form of a/b where a and b are the integer.

a/b=5+2√3

a/b-5=2√3

a-5b/b = 2√3

a-5b/2b=√3

5+2√3 is a irrational no. our assumption is wrong beacause a rational no. is never equal to the irrational no.

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Answer 2

Answer:

$2 \sqrt{3} = \frac{p}{q} - 5$

$2 \sqrt{3} = p - 5 \frac{q}{q }$

$\sqrt{3} = p - \frac{5q}{2q}$

so 5+2root3 is an irrational.