Prove that the real number
√
2 +
√5 is not rational.l​

2 thoughts on “Prove that the real number<br />√<br /> 2 +<br /> √5 is not rational.l​”

1. √2 + √5

   √2 value is 1.414..

   √5 value is 2.236…

   1.414..+2.236..

   = 3.65..

   it has a repeating decimal

   °°°° there fore it’s irrational number

   if it helps you drop a thanks

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2. Answer:

   Mark my answer as brainlist

   Step-by-step explanation:

   Prove that (root 2 + root 5 ) is irrational

   Given: √2+√5

   We need to prove√2+√5 is an irrational number.

   Proof:

   Let us assume that √2+√5 is a rational number.

   A rational number can be written in the form of p/q where p,q are integers and q≠0

   √2+√5 = p/q

   On squaring both sides we get,

   (√2+√5)² = (p/q)²

   √2²+√5²+2(√5)(√2) = p²/q²

   2+5+2√10 = p²/q²

   7+2√10 = p²/q²

   2√10 = p²/q² – 7

   √10 = (p²-7q²)/2q

   p,q are integers then (p²-7q²)/2q is a rational number.

   Then √10 is also a rational number.

   But this contradicts the fact that √10 is an irrational number.

   Our assumption is incorrect

   √2+√5 is an irrational number.

   Hence proved.

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