Question

given that ✓3 is an irrational number,prove that (2+✓3) is an irrational number

Answer 1

Hey there!!

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There exists a Theorem:

✔️If a Given Number is Irrational, Then anything added / Subtracted / Divided / Multiplied is always an irrational number,

Hence when √3 is already a Given Irrational number, So We will skip proving it

And ACC.to Foresaid Theorem,

2+√3 will also be an irrational!

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Thanks!!

Hope This Helps!

Have a great day dear! :)

Answer 2

Using a+b^2 = (a^2+b^2+2ab)

Here, a = 2, b =✓3

Therefore, (2+✓3)^2 = (2)^2 + (✓3)^2 + 2(2)(✓3)

                                 = 4+3+4✓3

                                 = 7+4✓3                                  

Answer = (2+✓3)^2 = 7+4✓3

(7+4✓3) is irrational because (✓3) is irrational..

Hence is it proved that (2+✓3) is an irrational number.