Question

14+6sqrt5=?
a)2+sqrt5 b) 3+sqrt5 c) 5+sqrt3 d)3+2sqrt5

Answer 1

Something is wrong. None of these answers are right.

Answer 2

Let 14+6sqrt5 be (a+sqrtb)^2

Answer 3

\[\begin{array}{rcl}
14+6\sqrt5&=&(a+\sqrt b)^2\\
14+6\sqrt5&=&a^2+b+2a\sqrt b\\
a^2+b=14&&2a\sqrt b=6\sqrt5
\end{array}\]

Answer 4

\[4a^2b=180\]\[a^2b=45\]

Answer 5

a^2=9 & b=5

Answer 6

Therefore it's the option b

Answer 7

CHECK:\[(3+\sqrt5)^2=9+2\cdot3\sqrt5+5=14+6\sqrt5\]