Question

prove 2+√3 is irrational number



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Answer 1

Answer:

3 square root is 1.7320508076

2 + 3 = 5 and 5 square root is 2.2360679775

these are considered as irrational numbers

Answer 2

Answer:

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Explanation:

We have to prove that 2+√3 is an irrational number

So, let 2+√3 is a rational number (r)

2+√3= r

(2+√3) whole squar= r *r ( squaring both sides)

4+3+2*2*√3 ( by opening the sqare)=r*r

7+4√3 =r*r

r*r-7=4√3

r*r-7/4=√3

Hence,r is a rational number

r*r is also a rational number

r*r-7 is also a rational number

r*r-7/4 is also a rational number

but, r*r-7/4 =√3

and we know that√3 is an irrational number

so our assumption gets wrong

2+√3 is an irrational number

*Hence proved*