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Question
Simplify the following by rationalizing the denominator.
3√5−√72√3+√2
3√5−√72√3+√2
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Solution
Given 3√5−√72√3+√2=3√5−√72√3+√2×2√3−√22√3−√2=(3√5−√7)(2√3−√2)(2√3)2−(√2)2
=(6√15−3√10−2√21+√14)12−2
=(6√15−3√10−2√21+√14)10
3√5−√72√3+√2
=3√5−√72√3+√2×2√3−√22√3−√2
=(3√5−√7)(2√3−√2)(2√3)2−(√2)2
=(6√15−3√10−2√21+√14)12−2
=(6√15−3√10−2√21+√14)10
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