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Prove that 3 + 2√5 is an irrational number
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♧︎︎︎ ǫᴜᴇsᴛɪᴏɴ ♧︎︎
- Prove that 3 + 2√5 is an irrational number
♧︎︎︎ ᴀɴsᴡᴇʀ ♧︎︎︎
➪ᴡᴇ ʜᴀᴠᴇ ᴛᴏ ᴘʀᴏᴠᴇ 3+2√5 ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ
ʟᴇᴛ ᴜs ᴀssᴜᴍᴇ ᴛʜᴇ ᴏᴘᴘᴏsɪᴛᴇ
ᴛʜᴀᴛ ɪs 3+2√5 ɪs ʀᴀᴛɪᴏɴᴀʟ
ʜᴇɴᴄᴇ,
sɪɴᴄᴇ,ʀᴀᴛɪᴏɴᴀʟ ≠ɪʀʀᴀᴛɪᴏɴᴀʟ
ᴛʜɪs ɪs ᴀ ᴄᴏɴᴛʀᴅɪᴄᴛɪᴏɴ
ᴛʜᴇʀᴇ ғᴏʀᴇ ,ᴏᴜʀ ᴀssᴜᴍᴘᴛɪᴏɴ ɪs ɪɴᴄᴏʀʀᴇᴄᴛ
ʜᴇɴᴄᴇ 3+23+2√5 ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ
ʜᴇɴᴄᴇ ᴘʀᴏᴠᴇᴅ
ɪ ʜᴏᴘᴇ ᴛʜɪs ʜᴇʟᴘs ᴜʜʜ
ᴍᴀʀᴋ.ᴀs ʙʀᴀɪɴʟᴇᴀsᴛ ☘︎
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.