Question

Prove that √5+√2 is irrational

proof by contradiction method​

Answer 1

Step-by-step explanation:

Use proof by contradiction. Assume that the sum is rationial, 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 −2√2ab +2.

Now, carefully solve for

√2 and obtain

√2=−3b 2a +a2b.

This implies that

√2 is a rational number which is a contradiction. Thus

√2+√5

is an irrational number.

Answer 2

Step-by-step explanation:

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