When a problem includes both a square root and an exponent, which operation should you evaluate first according to the standard order of operations?

When a problem includes both a square root and an exponent, which operation should you evaluate first according to the standard order of operations?

• A. Take the square root first
• B. Do whatever comes first in the problem
• C. Evaluate exponents before square roots
• D. Multiply or divide from left to right

Answer: (B)

Exponents come before square roots in the standard order of operations. When an expression inside a group has a power and a square root, you first evaluate the exponent, then apply the square root to the result. For example, in sqrt(3^2 + 4), you compute 3^2 to get 9, add 4 to get 13, and then take the square root to get sqrt(13). The placement of the operations matters: if you see (sqrt(3))^2, you would take the square root of 3 first and then square the result, giving 3. The main point is that exponents inside a radicand are resolved before the square root is applied.

Exponents come before square roots in the standard order of operations. When an expression inside a group has a power and a square root, you first evaluate the exponent, then apply the square root to the result. For example, in sqrt(3^2 + 4), you compute 3^2 to get 9, add 4 to get 13, and then take the square root to get sqrt(13). The placement of the operations matters: if you see (sqrt(3))^2, you would take the square root of 3 first and then square the result, giving 3. The main point is that exponents inside a radicand are resolved before the square root is applied.