Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 41
Chapter 1, Problem 41

Find each root. 25k4m2\(\sqrt{25k^4m^2}\)

Verified step by step guidance
1
Identify the expression inside the square root: \(\sqrt{25k^{4}m^{2}}\).
Recall the property of square roots that \(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\), so rewrite the expression as \(\sqrt{25} \cdot \sqrt{k^{4}} \cdot \sqrt{m^{2}}\).
Find the square root of each part separately: \(\sqrt{25}\), \(\sqrt{k^{4}}\), and \(\sqrt{m^{2}}\).
Use the rule \(\sqrt{x^{2}} = |x|\) to simplify the variable terms, so \(\sqrt{k^{4}} = |k^{2}|\) and \(\sqrt{m^{2}} = |m|\).
Combine all simplified parts to express the root as \(5 \cdot |k^{2}| \cdot |m|\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Square Root of a Product

The square root of a product can be expressed as the product of the square roots of each factor. For example, √(ab) = √a × √b. This property allows us to simplify complex expressions by breaking them into simpler parts.
Recommended video:
02:20
Imaginary Roots with the Square Root Property

Square Root of Variables with Exponents

When taking the square root of variables with exponents, divide the exponent by 2. For instance, √(x^n) = x^(n/2). This helps simplify expressions involving powers, especially when the exponent is even.
Recommended video:
02:20
Imaginary Roots with the Square Root Property

Simplifying Square Roots of Perfect Squares

A perfect square is a number or expression that is the square of an integer or variable expression. The square root of a perfect square is the base itself, such as √25 = 5 or √(k^4) = k^2, which simplifies the expression significantly.
Recommended video:
02:20
Imaginary Roots with the Square Root Property
Related Practice
Textbook Question

Find each product. (x+1)(x+1)(x-1)(x-1)

1
views
Textbook Question

Determine whether each statement is true or false. 1 ∈ {11, 5, 4, 3, 1}

Textbook Question

Factor each trinomial, if possible. See Examples 3 and 4. 9x2+4x−29x^2+4x-2

2
views
Textbook Question

Find each root.x66\(\sqrt\)[6]{x^6}

3
views
Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. 75÷310\(\frac\)75\(\div\]\frac{3}{10}\)

Textbook Question

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. (1/3)-2