Question

the sum of a number and its positive square root is 72 . find the number.

Answer 1

let the square root of number be X
thus no. be x^2
ACC to question
x^2+X=72
x^2+x-72 =0
x^2+9x-8x-72= 0
X(X+9)-8(X+9)= 0
X=-9 or X =8
but X=-9 is neglected as square root of a number can not be negative
thus number x^2 = 8^2 = 64

Answer 2

let the number be x
$x + \sqrt{x} = 72 \\ \sqrt{x } = 72 - x \\ squaring \: \: both \: sides$
$x = ( {72 - x)}^{2} \\ x =5184 + {x}^{2} - 144x \\ {x}^{2} - 145x + 5184 = 0$
${x}^{2} - 81x - 64x + 5184 = 0 \\ x(x - 81) - 64(x - 81) = 0 \\ (x - 81)(x - 64) = 0 \\ x = 81 \: \: \: x = 64$
from these value of x ,x =64 satisfies the equation.
$64 + \sqrt{64} = 72$
the number is 64.