True or False:
$\sqrt{9+16}$ and $\sqrt{9}+\sqrt{16}$ are equal.

• A. True
• B. False
• C. Cannot be determined

Answer: (B)

Verified step by step guidance

1. Identify the two expressions to compare: the square root of the sum (\sqrt{9 + 16}) and the sum of the square roots (\sqrt{9} + \sqrt{16}).
2. Calculate the value inside the first square root: 9 + 16, which simplifies to 25, so the first expression is \sqrt{25}.
3. Calculate the square root of 25, which is a single value (but do not finalize the numeric result as per instructions).
4. Calculate each square root separately in the second expression: \sqrt{9} and \sqrt{16}, then add these two results together.
5. Compare the two results conceptually: understand that \sqrt{a + b} is generally not equal to \sqrt{a} + \sqrt{b} unless specific conditions hold, so determine if the two expressions are equal or not.