Question

show that 2+ root5 is irrational number​

Answer 1

Answer:

Step-by-step explanation:

Let's find if √2 + √5 is irrational.

Explanation:

To prove that √2 + √5 is an irrational number, we will use the contradiction method.

Let us assume that √2 + √5 is a rational number with p and q as co-prime integers and q ≠ 0

⇒ √2 + √5 = p/ q

Squaring both sides:

⇒ 7 + 2√10 = p2/q2

⇒ √10 = (p2/q2 - 7) / 2

⇒ We know that (p2/q2 - 7) / 2 is a rational number.

Also, we know √10 = 3.1622776... which is irrational.

Since we know that √10 is an irrational number, but an irrational number cannot be equal to a rational number.

This leads to a contradiction that √2 + √5 is a rational number.

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Answer 2

Answer:

Let 2+√5 be a rational number

2+√5= a\b [ where a and b are integers]

√5=a/b-2/1

√5=a-2b/b

So,a-2b/b is a rational number

we can say that √5 should also be a rational number

But,this contradicts the fact that √5 is a irrational number

So,our assumption was wrong

Since,we can say that 2+√5 is a irrational number

Step-by-step explanation:

First you have to take 2+√5 a rational number,then you have write the criteria needed for a rational number is a/b form where b isn't equal to 0