Question

prove that root 6 plus root 5 is irrational​

Answer 1

Answer:

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Step-by-step explanation:

This question can be solved in two ways.

1)Let us assume, to the contrary, that √5+√6 is irrational.

So we can find two integers numbers a and b(≠0), in the following way,

√5+√6 = a/b

Rearranging,

√5 = a/b - √6

= integer/integer - rational ...( as √6 is assume as rational)

So, this means that √5 is rational.

But this contradict the fact that √5 is irrational.

Our assumption is wrong.

Hence, √5 + √6 is irrational.

2) Let us assume, to the contrary, that √5+√6 is irrational.

So we can find two integers numbers a and b(≠0), in the following way,

√5+√6 = a/b

Rearranging,

√6 = a/b - √5

= integer/integer - rational ...( as √5 is assume as rational)

So, this means that √6 is rational.

But this contradict the fact that √6 is irrational.

Our assumption is wrong.

Hence, √5 + √6 is irrational.

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