The square root of 11+root112 is - Maths - Mathematical Reasoning

Question

The square root of 11+root112 is?

Komal Garg · Accepted Answer

Dear student, Answer: The answer is √7 + 2 Step-by-step explanation: Here, the given expression is, $11 + sqrt{112}$ , $= 11 + sqrt{4times 28}$ $= 11 + sqrt{4} times sqrt{28}$ $= 11 + 2 times sqrt{28}$ $= 11 + 2 times sqrt{7} times sqrt{4}$ $= 7 + 4 + 2 times sqrt{7} times sqrt{4}$ $= (sqrt{7})^2 + (sqrt{4})^2 + 2times sqrt{7}times sqrt{4}$ $= (sqrt{7} + sqrt{4})^2$ [identity used: (a+b)2 = a2 +b2 + 2ab] Thus, 11 + √112 = (√7 + √4)² Hence, $sqrt{11+sqrt{112}}=sqrt{(sqrt{7}+sqrt{4})^2}=sqrt{7}+sqrt{4}=sqrt{7}+2$ Regards