step 1 So in this question we're given the square root of 75, which we can rewrite as the square root o

Question

Simplify. $$\sqrt{75}$$

   Simplify.
$$\sqrt{75}$$

McDougal Littell Jurgensen Geometry : Student Edition 2000

Ray C. Jurgensen,… 1st Edition

Chapter 8, Problem 4

Instant Answer

Solved by Expert K B

08/30/2019

Step 1

75 can be factored into 3 and 25, where 25 is a perfect square. So, 75 = 3 × 25. Show more…

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Simplify. $$\sqrt{75}$$

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Key Concepts

Perfect Squares

A perfect square is an integer that can be expressed as the square of another integer. Identifying perfect square factors within a radicand is crucial in the simplification process, as taking the square root of a perfect square yields an integer, thus simplifying the overall expression.

Properties of Radicals

This concept involves the rules for manipulating radical expressions, such as the product rule which states that the square root of a product can be written as the product of the square roots. This property is essential when simplifying expressions that involve square roots.

Factorization

Factorization is the process of breaking down a number or expression into a product of simpler factors. When simplifying radicals, factorization allows one to express the radicand as a product, and to identify and separate perfect square factors from those that remain under the radical.

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