Question

√14+6√5=a+√b then find a+b

Answer 1

Here is your answer check it iwhether it is right or wrong.

Answer 2

Answer:

its answer is "8".

Step-by-step explanation:

          $\sqrt{14 + 6\sqrt{5} } = a + \sqrt{b}$

=> $\sqrt{14 + 2.3.\sqrt{5} } = a + \sqrt{b}$ [Here, 6 is factorized in its shortest form so that in $2^{nd}$ step we get " 2.a.b " in which "a" is "3" and "b" is  "$\sqrt{5}$ " respectively.]

=>  $\sqrt{3^{2} + \sqrt{5} ^{2} + 2.3.\sqrt{5} } = a + \sqrt{b}$ [Here the formula $(a + b )^{2}$= $a^{2} + b^{2} + 2.a.b$  the L.H.S   . Here you can understand better if you go through $3^{rd}$ step to $2^{nd}$ step]

                                                                                                                                                                             

   =>   $\sqrt{( 3 + \sqrt{5 )} ^ {2}$= a + $\sqrt{b}$

   =>  3 + $\sqrt{5}$  =  a + $\sqrt{b}$

   Compairing "a" and "$\sqrt{b}$" with "3" and "$\sqrt{5}$" respectively.

      Therefore,      a = 3    and        $\sqrt{b}$ = $\sqrt{5}$

                                                      => b = 5

   

        So,       ( a+b ) = 3 + 5    

                   => ( a+b ) = 8