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

Verified step by step guidance

1. Recognize that the problem involves square roots of perfect squares: \(\sqrt{25}\) and \(\sqrt{64}\).
2. Recall that \(\sqrt{25}\) is the number which, when squared, gives 25. Similarly, \(\sqrt{64}\) is the number which, when squared, gives 64.
3. Identify the values of these square roots: \(\sqrt{25} = 5\) and \(\sqrt{64} = 8\).
4. Add the two results together: \$5 + 8$.
5. Write the final answer as the sum of these two numbers without intermediate calculations.

Key Concepts

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √25 equals 5 because 5 × 5 = 25. Understanding square roots helps simplify expressions involving radicals.

Simplification of Radicals

Simplifying radicals involves finding the simplest form of a square root or other root expression. Recognizing perfect squares like 25 and 64 allows quick simplification to integers, making mental calculations easier.

Mental Arithmetic with Radicals

Performing operations mentally requires familiarity with common square roots and basic arithmetic. Adding simplified square roots directly, such as 5 + 8, helps solve problems quickly without writing intermediate steps.