Find each root. √25k⁴m²

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 × 5 = 25. In algebra, square roots can also apply to variables, where the square root of a variable raised to an even power can be simplified by halving the exponent.

Exponent Rules

Exponent rules are mathematical guidelines that dictate how to handle expressions involving powers. For instance, when taking the square root of a variable raised to an exponent, you divide the exponent by 2. This is crucial for simplifying expressions like √(k⁴) to k², as it allows for easier manipulation of algebraic terms.

Simplifying Radical Expressions

Simplifying radical expressions involves reducing the expression under the square root to its simplest form. This includes factoring out perfect squares and applying the square root to each factor. For example, √(25k⁴m²) can be simplified to 5k²m, as both 25 and k⁴ are perfect squares, making the expression easier to work with in further calculations.