Question

Prove that √2+√11 is a irrational number

Answer 1

Suppose ✓2+√11is the rational number and can be written as in the form of p/q

√2+√11=p/q

squaring both side

(√2+√11)^2=(p/q)^2

2+11+2√22=(p/q)^2

2√22=(p/q)^2-13

√22=1/2(p/q)^2-13

we know that √22 is the irrational number

which is the contradiction with the fact that √2+√11is the irrational number

Answer 2

Hey there!

Here is your answer

Let √2+√11 =a,where a is a rational .

Therefore,√2=a-√11

On squaring on both sides,we get

(√2)^2=(a-√11)^2

2=a^2+11-2a√11

2a√11=a^2+9

√11=a^2+9/2a which is contradiction;

As the right hand side is rational number while √11 is irrational.

Hence √2+√11 is irrational

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Hope it helps!

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