Question

prove 7+3 under root 3 is irrational number

Answer 1

If the question is too number then you also do √3 is irrational then you will meet 4marks

Answer 2

Heya
Here is your answer 
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If we add, multiply, divide, subtract anything from any irrational number then the whole no. becomes irrational so we just have to prove √3 irrational
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Here is the process:

Let √3 is rational no. a/b where a and b are co-prime

cross multiplying √3 and a/b

a = √3b

Squaring both sides

a² = 3b² ⇒ Equation 1

a²/3 = b²

⇒3 divide a²
⇒3 divide a

Putting a = 3c in equation 1

(3c)² = 3b²

9c² = 3b²

3c² = b²

c² = b²/3

⇒3 divide b²
⇒3 divide b



3 divide both a and b and our assumption was wrong.
So we conclude that √3 is irrational and hence 7+3√3  is irrational

Hence Proved.
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Hope it helps! ^_^