Question

rationalize the denominator and evaluate root 2 by 2 + root 2 by taking root 2 is equal to 1.414 upto 3 decimal places

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ

2 / ( 2 + √2 )

ʀᴀᴛɪᴏɴᴀʟɪᴢᴇ

2 / ( 2 + √2 ) × ( 2 - √2 ) / ( 2 - √2 )

2( 2 - √2 ) / ( 2² - √2² )

2( 2 - √2 ) / ( 4 - 2 )

= 2 ( 2 - √2 ) / 2

2 ɢᴏᴛ ᴄᴀɴᴄᴇʟʟᴇᴅ ᴏᴜᴛ

= 2 - √2

2 - 1.414 = 0.586

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs

Answer 2

$\frac{2}{2 + \sqrt{2 } } = \frac{2(2 - \sqrt{2)} }{(2 + \sqrt{2})(2 - \sqrt{2)} } = \frac{2(2 - \sqrt{2} )}{ {2}^{2} - { \sqrt{2} }^{2} } = \\ \frac{2(2 - \sqrt{2} )}{4 - 2} = \frac{2(2 - \sqrt{2} )}{2} = 2 - \sqrt{2 } = \\ 2 - 1.414 = 0.586$
Hope this is the right answer!!!