Question

Find the positive square root of 16+2root55

Answer 1

Step-by-step explanation:

Let (√x+√y) is the positive square root of (16+2√55) , accordingly :-

(√x+√y)^2 = 16 + 2√55.

or, x +y +2.√(x.y) = 16 + 2√55.

Thus, x + y = 16. …………………(1)

x. y = 55. …………………………..(2).

Putting y = 16 - x from eqn. (1) in eqn.(2)

x.(16 - x) = 55.

or, x^2 -16 .x + 55 = 0.

or, (x-5).(x-11) = 0.

or, x = 5. , 11. , putting the values of x in y= 16 - x. , y = 11 , 5.

Thus , the positive square root of 16 + 2√55 are (√5+√11) or (√11+√5) which

are same. So , (√11+√5). Answer.

Answer 2

Step-by-step explanation:

Let (√x+√y) is the positive square root of (16+2√55) , accordingly :-

(√x+√y)^2 = 16 + 2√55.

or, x +y +2.√(x.y) = 16 + 2√55.

Thus, x + y = 16. …………………(1)

x. y = 55. …………………………..(2).

Putting y = 16 - x from eqn. (1) in eqn.(2)

x.(16 - x) = 55.

or, x^2 -16 .x + 55 = 0.

or, (x-5).(x-11) = 0.

or, x = 5. , 11. , putting the values of x in y= 16 - x. , y = 11 , 5.

Thus , the positive square root of 16 + 2√55 are (√5+√11) or (√11+√5). Answer