Math, asked by Mbappe007, 1 month ago

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Prove that 3 + 2√5 is an irrational number

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Answers

Answered by Limafahar
5

♧︎︎︎ ǫᴜᴇsᴛɪᴏɴ ♧︎︎

  • Prove that 3 + 2√5 is an irrational number

♧︎︎︎ ᴀɴsᴡᴇʀ ♧︎︎︎

ʜ ʀ 3+2√5 ɪs ɪʀʀɪɴʟ

ʟ s ss ʜ sɪ

ʜ ɪs 3+2√5 ɪs ʀɪɴʟ

ʜɴ,

3+2√5= \frac{a}{b}

2 \sqrt{5}  =  \frac{a}{b}  - 3

2 \sqrt{5}  =  \frac{a - 3b}{b}

 \sqrt{5}  =  \frac{1}{2}  \times  \frac{a - 3b}{b}

here \: \frac{a - 3b}{2b} is \: a \: rational \: number

but \:  \sqrt{5}  \: is \: irrational

sɪɴ,ʀɪɴʟ ɪʀʀɪɴʟ

ʜɪs ɪs ɴʀɪɪɴ

ʜʀ ғʀ ,ʀ ssɪɴ ɪs ɪɴʀʀ

ʜɴ 3+23+2√5 ɪs ɪʀʀɪɴʟ

ʜɴ ʀ

ɪ ʜ ʜɪs ʜʟs ʜʜ

ʀ.s ʙʀɪɴʟs ☘︎

Answered by CopyThat
36

Answer :-

3 + 2√5 is an irrational number.

Step-by-step explanation :-

Given :

3 + 2√5

To prove :

3 + 2√5  is an irrational number.

Solution :

Lets assume 3 + 2√5 as a rational number, so it can be written in the form a/b where a and b are co-prime and b ≠ 0.

So we get :

3 + 2√5 = a/b

2√5 = a/b - 3

2√5 = (a - 3b)/b

√5 = (a - 3b)/2b

We know that :

√5 is irrational.

(a - 3b)/2b is rational.

A rational number cannot be equal to irrational number.

∴ 3 + 2√5 is an irrational number.

Learn more :

https://brainly.in/question/39845938

To prove that 5 - √3 is irrational number.

https://brainly.in/question/41964165

To prove that √5 - 2 is irrational number.

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