Simplify. √(49 n^17)

Name: Problem 73, Chapter 9: Elementary Algebra
Uploaded: 2021-07-16T15:11:49-08:00
Duration: 1 min 32 s
Channel: Chris Wojturski
Description: Simplify. √(49 n^17)

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Key Concepts

Square Root Properties

Square roots follow the rule that the square root of a product is the product of the square roots, provided that all quantities are nonnegative. This property allows us to split a complex radical into more manageable parts where perfect squares can be simplified separately.

Exponent Rules

When dealing with variables raised to a power under a square root, it is useful to separate the exponent into an even and an odd part. The even power corresponds to a perfect square, allowing it to be taken out of the radical, while the remainder stays under the square root.

Perfect Squares

A perfect square is an expression that can be written as the square of another expression. Identifying perfect square factors within a radicand enables us to simplify radicals by extracting these factors and reducing them to their base expressions outside the square root.

Simplifying Radical Expressions

Simplifying a radical involves factorizing the radicand into factors that include perfect squares and remaining factors. Once the perfect square factors are identified, their square roots can be computed and moved outside the radical, resulting in a more simplified expression.

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