Question

√7+√3 is a rational no.or irrational give answer with explain

Answer 1

Hi there !!

✓7 + ✓3 is irrational !
Wondering how and why ??

Here's the explanation :)

We know that ,
✓7 = 2.64575...... [ This continues till infinity and no sequence is repeating ]
✓3 = 1.732050.... [ This is also never ending and never recurring ]

When we add ✓7 + ✓3
We get ,
2.64575... + 1.732050..
= 4.377801.... [ approx. ]

This number will continue till infinity , i.e , it is non terminating and will never be repeating , i.e , non recurring

By definition, we know that a number is said to be irrational if it is non terminating and non repeating.
Here , ✓7 + ✓3 satisfies all the conditions. Hence it is irrational.

__________

Hope it helps :D

Answer 2

heya

here is ur answer

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✴ another method

✒ let us assume the contradict.√7+√3 as rational

✒if it is rational then it must be of form a/b , where a,b are integers and b≠ 0.

✒ √7+√3 = a/b

✒√7 = a/b - √3

▶ squaring on both sides

(√7)^2 = ( a/b - √3) ^ 2

▶ using (a-b )^2 formula on RHS

✒ 7 = a^2/b^2 + (√3)^2 - 2.a/b.√3

✒ 7 = a^2/b^2 + 3 - 2a/b.√3

▶on rearrange the terms.

✒ 2a/b.√3 = a^2 / b^2 + 3 -7

✒2a/b .√3 = a^2/b^2 -4

✒ 2a/b .√3 = a^2 - 4b^2/b^2

✒ 2a.√3 = a^2-4b^2/b^2- b

✒ 2a.√3 = a^ 2- 4b^2 /b

✒ √3 = a^2- 4b^2 /2ab

⏩ finally v got √3 on LHS

⏩ v know that a irrational number is never equal to a rational number .

⏩ so this is because of our wrong assumption that √7+√3 as a rational number.

⏩ so finally v draw a conclusion that √7 +√3 as a irrational number

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hope it helps u

thnkq ^_^