Question

The sum of a natural number and its positive square root is 132 find the number

Answer 1

The number is 121, because 121 +121^0.5 = 121 + 11 = 132.

Let the number be x. Then x +x^0.5 = 132, or

Let x = y^2, so we have

y^2+y-132=0

(y-11)(y+12)=0, or

y = 11 or -12, or

x - 121 or 144 (ruled out)

So x = 121.

Answer 2

Hey

Here is your answer,

Answer:

Let the required natural number be x.

According to the given condition,

x + x2 = 156

x2 + x -156 =0

x2 + 13x – 12x — 156 = 0

x(x + 13) – 12(x + 13) = 0

(x + 13)(x — 12) = 0

x + 13 = 0 or x – 12 = 0

x = -13 or x = 12

Therefore, x = 12 (x cannot be negative)

Hence, the required natural number is 12.

Hope it helps you!