In Exercises 33–46, simplify each expression. __ √5²

Verified step by step guidance

1. Recognize that the expression involves a square root and a square: $\sqrt{5^2}$.
2. Recall the property of square roots: $\sqrt{a^2}=|a|$, which means the square root of a square is the absolute value of the original number.
3. Apply this property to the expression: $\sqrt{5^2}=|5|$.
4. Since 5 is a positive number, the absolute value of 5 is simply 5.
5. Conclude that the simplified expression is 5.

Key Concepts

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. In this context, the square root symbol (√) indicates that we are looking for a number that, when multiplied by itself, gives the original number. For example, √25 = 5 because 5² = 25.

Properties of Exponents

The properties of exponents govern how to manipulate expressions involving powers. One key property is that (a^m)² = a^(2m), which means squaring a number raised to a power doubles the exponent. This is essential for simplifying expressions like √(a²) = a, where 'a' is a non-negative number.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form. This can include combining like terms, applying the distributive property, and using square roots and exponents. In the case of √5², simplification leads to the result of 5, as the square root and the square cancel each other out.