Question

Rationalize 2/(14−2√6)​

Answer 1

Answer:

7−√6 / 43

Step-by-step explanation:

2/(14−2√6)​ * (14+2√6)​/(14+2√6)​

2 * (14+2√6)​/ (14-2√6)​ * (14+2√6)​

28+4√6 / 14*14 - 2√6*2√6

28+4√6 / 196 - 4*6

28+4√6 / 196 - 24

28+4√6 / 172

2(14+2√6) / 2(86)

14−2√6 / 86

2(7−√6) / 2(43)

7−√6 / 43

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Answer 2

ɢɪᴠᴇɴ:

$\frac{2}{14 - 2 \sqrt{6} }$

ᴛᴏ ꜰɪɴᴅ:

Rationalised form

ꜱᴏʟᴜᴛɪᴏɴ:

$→\frac{2}{14 - 2 \sqrt{6} } =\frac{2}{14 - 2 \sqrt{6} } \times \frac{14 + 2 \sqrt{6} }{14 + 2 \sqrt{6} } \\ \\ →\frac{2}{14 - 2 \sqrt{6} } = \: \: \: \frac{2 \times (14 + 2 \sqrt{6} )}{ {(14)}^{2} - {(2 \sqrt{6}) }^{2} } \: \: \: \: \: \: \: \: \: \: \\ \\ →\frac{2}{14 - 2 \sqrt{6} } \: = \: \frac{2 \times (14 + 2 \sqrt{6}) }{196 - 24} \: \: \: \: \: \: \: \: \: \: \: \\ \\ →\frac{2}{14 - 2 \sqrt{6} } = \frac{2 \times (14 + 2 \sqrt{6}) }{172} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ →\frac{2}{14 - 2 \sqrt{6} } = \frac{14 + 2 \sqrt{6} }{86} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ →\frac{2}{14 - 2 \sqrt{6} } = \frac{2 \times (7 + \sqrt{6}) }{2 \times 43} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ →\frac{2}{14 - 2 \sqrt{6} } \: = \frac{7 + \sqrt{6} }{43} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$