Final answer:
Two square root expressions with values greater than 5 are √36 and √49. These expressions yield the numbers 6 and 7, respectively, both of which are greater than 5. Square roots can also be represented by raising a number to the power of 0.5.
Step-by-step explanation:
To write two square root expressions that have a value greater than 5, we need to consider numbers that when squared are greater than 25, since the square root of 25 is 5 and we are looking for a larger value. An example of such an expression is √36, because 6² = 36 and the square root of 36 is 6, which is greater than 5.
Another expression is √49, because 7² = 49 and the square root of 49 is 7. Both of these expressions, when simplified, result in values greater than 5.
Remember that raising a number to the power of 0.5 is the same as taking the square root, as seen in the identity x² = √x. For instance, 6² = 6×1 = 36, then taking the square root, which is raising it to the power of 0.5, we return to the original number, 6. This principle helps us understand square roots and manipulate them algebraically.