square root of 49 + 20 root 6
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3 Answers
Sylar Kumar, studied at National Institute of Technology, Patna
Answered November 19, 2018 · Author has 123 answers and 27.3K answer views
Since it is a surd, we know that hte square root of this value is a surd represented by a+b6–√a+b6 , where a and b are integers to solve for.
Thus
(a+b6–√)2=49+206–√(a+b6)2=49+206
a2+6b2+2ab6–√=49+206–√a2+6b2+2ab6=49+206
Thus a2+6b2=49a2+6b2=49
and 2ab=202ab=20
Thus ab=10ab=10
Solve the quadratic equation (10/b)2+6b2=49(10/b)2+6b2=49
we get
6b4–49b2+100=06b4–49b2+100=0
6b4–24b2–25b2+100=06b4–24b2–25b2+100=0
6b2(b2−4)−5(b2−4)=06b2(b2−4)−5(b2−4)=0
We get b2=4b2=4 or b2=5/6b2=5/6
Thus b=2,−2,5/6−−−√,−5/6−−−√b=2,−2,5/6,−5/6
Thus, the corresponding values of aa can be
5,−5,230−−√,−230−−√5,−5,230,−230
Thus, the possible answers are
5+26–√5+26
−5−26–√−5−26