Question

The value of square root of 15 + 2√56 = a +√b where a and b are integers then a + b =

Answer 1

Looks like there is a correction in question. It is solved wrt correct one.

Answer:

15

Step-by-step explanation:

$\implies \sqrt{15+2\sqrt{56}}=\sqrt a+\sqrt b\\\\\implies\sqrt{7+8+2\sqrt{8*7}}=\sqrt a+\sqrt b\\\\\implies \sqrt{(\sqrt{7})^2+(\sqrt{8})^2+2\sqrt{8*7} }=\sqrt a+\sqrt b$

 Using a^2 +  b^2 + 2ab = ( a + b )^2   { for LHS }

$\implies\sqrt{(\sqrt7 + \sqrt8 )^2} =\sqrt a + \sqrt b\\\\\implies \sqrt7 + \sqrt8 = \sqrt a + \sqrt b$

Hence a + b = 7 + 8 = 15