Question

show that √5 + √2 is irrational​

Answer 1

Answer:

Step-by-step explanation

Use proof by contradiction. Assume that the sum is rational, that is

2–√+5–√=ab

where a and b are integers with b≠0. Now rewrite this as

5–√=ab−2–√.

Squaring both sides of this equation we obtain

5=a2b2−22–√ab+2.

Now, carefully solve for 2–√ and obtain

2–√=−3b2a+a2b.

This implies that 2–√ is a rational number which is a contradiction. Thus

2–√+5–√

is an irrational number.