Question

Find the positive square root of 11+√112 ? give me the answer with explanation quickly​

Answer 1

Answer:

+-(2 +√7)

Step-by-step explanation:

Lets look at it like this

let a + b be the square root of 11 + √112

Then (a+b)^2 = 11+√112

a^2 + b^2 + 2ab= 11 + √112

Now assume that a is the rational part and b is the irrational part{square root of a number}

Hence b^2 is a rational number

And 2ab is irrational {rational times irrational is irrational}

Hence compare the rational and irrational parts on both sides

a^2 +b^2 =11 and 2ab=√112

From 2nd equation

a=√112/(2b)

a= √28/b

Put in first equation

28/(b^2) + b^2 =11

b^4 -11b^2 +28 =0

Let x=b^2

x^2 -11x +28 =0

Solving this equation,

x= 7 or 4

Hence b= +-√7 or +-2

Put this in equation 2 Again

a= √28/b

So a= +-2 or +-√7

Hence the square root of 11+√112 is

+-(2 +√7)

Answer 2

Answer:

-932622 is the answer of 11+✓ 112