Question

The square root of the difference of a number and 12, added to the square root of the number is 6. Determine the number.

Answer 1

Question

The difference between a number and its positive square root is 12. What is the number?

Answer · 5 votes

Consider [math]x - \sqrt{x} = 12[/math]. Let [math]y = \sqrt{x}[/math] and by

Answer 2

Given,

For a certain number, the square root of the difference of the number and 12, added to the square root of the number is 6.

To find,

The certain number.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the certain number is x.

Now, according to the question;

√(x-12) + √x = 6

=> √(x-12) = (6-√x)

=> (6-√x)^2 = x-12

=> (6)^2 + (√x)^2 - 2(6)(√x) = x - 12

{according to the algebraic identity:

(a-b)^2 = a^2 + b^2 - 2ab}

=> 36 + x - 12√x = x - 12

=> 12√x = 48

=> √x = 4

=> x = (4)^2

=> x = 16

Hence, the required number is 16.