Question

Prove that root 5plus root 11 is irrational

Answer 1

Answer:

Let us consider √5 + √11 is not irrational

then it becomes √5 + √11 is a rational

we know that

p/q where p , q belongs to integers and q ≠ 0

Squaring on both sides

(√5 + √11 ) 2 = ( p/q ) 2

Use ( a + b ) 2 formula

(√5)2 + (√11)2 + 2 × √5 × √11 = p2 / q2

5 + 11 + 2 × √55 = p2 / q2

16 + 2 × √55 = p2 / q2

2 × √55 = p2 / q2 - 16 / 1

√55 = p2 - 16 q2 / q2

LHS = √11 where it is irrational because " 11 " is

not a perfect square .

RHS = p2 - 16 q2 / q2

It becomes rational because it is in the form of p/q

Our contradiction is wrong

Our Assumption is wrong

√5 + √11 is an irrational

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Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

root 5+ root 11= a/b

root5=  a-root11b/b

since, a-root11b/b is rational

root 5 shoild be rational

but LHS not = to RHS

our assumpyion is wrong.....

so, root 5 + root 11 is irrational,,,....!!!!