Question

prove 2+√7 is irrational ?​

Answer 1

Hi friend, Here's the required answer:-

Let us assume that 2/√7 is rational number.

2/√7= 2/√7 × (√7/√7)= 2√7/7. ( Rationalising)

Now, 2√7/7 = p/q ( as rational no. can be written in the form of p/q=)

2√7= 7p/q

√7= 7p/2q

Here LHS is irrational but RHS is rational.

This contradicts the statement.

Our assumption is wrong.

2/ √7 is an irrational number.

Answer 2

Step-by-step explanation:

Lᴇᴛ ᴜs ᴀssᴜᴍᴇ ᴛʜᴀᴛ 2/√7 ɪs ʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

2/√7= 2/√7 × (√7/√7)= 2√7/7. ( Rᴀᴛɪᴏɴᴀʟɪsɪɴɢ)

Nᴏᴡ, 2√7/7 = ᴘ/ϙ ( ᴀs ʀᴀᴛɪᴏɴᴀʟ ɴᴏ. ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ɪɴ ᴛʜᴇ ғᴏʀᴍ ᴏғ ᴘ/ϙ=)

2√7= 7ᴘ/ϙ

√7= 7ᴘ/2ϙ

Hᴇʀᴇ LHS ɪs ɪʀʀᴀᴛɪᴏɴᴀʟ ʙᴜᴛ RHS ɪs ʀᴀᴛɪᴏɴᴀʟ.

Tʜɪs ᴄᴏɴᴛʀᴀᴅɪᴄᴛs ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ.

Oᴜʀ ᴀssᴜᴍᴘᴛɪᴏɴ ɪs ᴡʀᴏɴɢ.

2/ √7 ɪs ᴀɴ ɪʀʀᴀᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ.

HOPE IT HELPS YOU OUT ❤

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