Question

I need help figuring out the answers to these kinda poorly worded questions

Answer 1

Answers:

• What is that positive integer?  400
• What is the value of the positive root?  20
• What is the value of the negative root?  -20

=======================================================

Explanation:

Let x be the unknown positive integer.

The square roots of x are $\sqrt{x}$ and $-\sqrt{x}$, representing the positive and negative square roots respectively.

Taking the difference of those means we subtract:

$\text{PositiveRoot}-\text{NegativeRoot} = \sqrt{x} - (-\sqrt{x}) = \sqrt{x}+\sqrt{x} = 2\sqrt{x}$

Set that equal to 40 and solve for x

$2\sqrt{x} = 40\\\\\sqrt{x} = 40/2\\\\\sqrt{x} = 20\\\\x = 20^2\\\\x = 400$

Therefore, the integer we're after is 400.

The positive square root of such is $\sqrt{x} = \sqrt{400} = \sqrt{20^2} = 20$

And the negative square root is $-\sqrt{x} = -\sqrt{400} = -\sqrt{20^2} = -20$

The difference of which is:

(Positive Root) - (Negative Root) = 20-(-20) = 20+20 = 40

This helps confirm the answers.