Final answer:
The unknown number in question is 7, as adding 7 to the square root of 5 yields the same sum as adding the square root of 5 to the unknown number, according to properties of equality and addition.
Step-by-step explanation:
The question is asking to deduce information about an unknown number when 7 is added to the square root of 5 (written as \(\sqrt{5}\)), and the sum is equivalent to \(\sqrt{5}\) plus this unknown number. By the properties of equality and addition, the unknown number must equal 7 since adding 7 to \(\sqrt{5}\) yields the same result as adding the unknown number to \(\sqrt{5}\). This can be seen clearly by setting up the equation \(7 + \sqrt{5} = \sqrt{5} + x\), where x is our unknown number, and then simplifying by subtracting \(\sqrt{5}\) from both sides to isolate x, thereby obtaining x = 7. Therefore, we know that the unknown number is 7.