Question

prove that 6+√2 is irrational stage of 10th standard

Answer 1

HEY YOUR ANSWER IS .....


Let us assume , to the contrary that 6+√2 is rational .

That is , we can find coprime a and b such that 6+√2 =a/b

Therefore , 6-a/b = -√2


So ,

-√2 = 6b-a/b

Since , a and b are integers , we get 6-a/b is rational and so -√2 is rational .

But this contradicts the fact that √2 is irrational.


Therefore , 6+√2 is irrational .


Hope it helps .....

Answer 2

Step-by-step explanation:

Given:

• 6+√2

To Prove:

• 6 + √2 is irrational

Solution:

† We have to prove 6+√2 is irrational †

→ Let us assume the opposite i.e 6+√2 is rational

• Hence, 6+√2 can be written in form of a/b. Where a and b( b≠0) are co-prime •

★ Hence, 6 + √2 = a/b ★

$\small\implies{\sf }$ √2 =a/b –6

• √2 ( Irrational ) = a–6b/b (Rational)

• Here, a – 6b/b is a Rational Number

• But, √2 is a Irrational

Since, Rational ≠ Irrational

★ This is a contradiction

• ∴ Our assumption is wrong

Hence, 6 + √2 is Irrational. Proved ✓