Final answer:
To find a number whose arithmetic square root is 'x', you square 'x' to get 'x²'. For example, the square of 3 is 9, as 3 squared equals 9. Extending the concept, similar methods apply to cube roots and other powers.
Step-by-step explanation:
The question seems to be about finding a number whose arithmetic square root (as misspelled 'arethemetic') matches a given condition or more simplistically, finding the square of a given number. If we consider the provided reference, we can similarly analyze the expression x² = √x. This implies that if 'x' is the arithmetic square root of 'x²', to find 'x²' you simply square 'x'. Therefore, applying this to a hypothetical value, if we have a number 'y' and we know its arithmetic square root is 'x', it follows that 'y = x²'.
To tackle an example question such as 'What is the square of 3?', we would simply calculate '3²', which equals 9. This demonstrates that 9 is the number whose arithmetic square root is 3. The process of squaring a number is a fundamental concept in mathematics, frequently used in various equations and real-world applications.
Regarding the additional information provided about powers and roots, these concepts can be employed to simplify expressions and solve equations that involve different degrees of roots, like square roots, cube roots, and fourth roots. If we extend beyond square roots, we may encounter equations that require a solution for cube roots (as implied by the reference to 'a³'), where the method to solve includes finding a value that, when raised to the third power (cubed), equals a given number.