CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps.√25 + √64

Verified step by step guidance

1. Identify the square roots: \( \sqrt{25} \) and \( \sqrt{64} \).
2. Recall that \( \sqrt{25} = 5 \) because 5 squared equals 25.
3. Recall that \( \sqrt{64} = 8 \) because 8 squared equals 64.
4. Add the results of the square roots: 5 + 8.
5. Write down the sum of the two numbers obtained from the square roots.

Key Concepts

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, since 5 x 5 = 25. Understanding square roots is essential for simplifying expressions involving radical signs.

Addition of Square Roots

When adding square roots, if the numbers under the radical signs are perfect squares, they can be simplified first. For instance, √25 simplifies to 5 and √64 simplifies to 8, allowing for straightforward addition of the resulting whole numbers.

Mental Math Techniques

Mental math involves performing calculations in your head without writing down intermediate steps. This skill is useful for quickly solving problems, such as adding simplified square roots, and requires practice to enhance speed and accuracy.