Question

prove that 3+2√5 is irrational In proving this do we need to first price that√5 is irrational???????​

Answer 1

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⬇️HERE IS YOUR ANSWER⬇️

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yeѕ, ιn provιng 3+2√5 ιrraтιonal, we нave тo prove √5 aѕ ιrraтιonal ғιrѕт.

вυт, ѕoмeтιмeѕ ιт'ѕ gιven ιn тнe qυeѕтιonѕ,

ιғ ιт'ѕ noт тнen prove √5 aѕ ιrraтιonal ғιrѕт.

HOPE THIS ANSWER HELPS YOU

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Answer 2

let us assume that 3+2√5 as rational number.

now,

3+2√5=a/b

√5=a/2b-5

here,

a/2b-5 is rational number

so √5 is also rational number

but, it is mentioned that √5 is irrational number.

so this contradiction has arisen due to our incorrect assumption

so 3+2√5 is irrational number.

hope it helps u