Textbook Question
CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x/5 + x/4
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 9
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6
Verified step by step guidance1
Recall the property of square roots that states: \(\sqrt{a} \times \sqrt{a} = a\) for any positive number \(a\).
Apply this property to the given expression \(\sqrt{6} \times \sqrt{6}\).
Since both square roots are of the same number 6, multiply them directly using the property: \(\sqrt{6} \times \sqrt{6} = 6\).
Understand that this operation simplifies the expression by removing the square root, leaving just the number inside.
Therefore, the result of \(\sqrt{6} \times \sqrt{6}\) is simply 6.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Roots and Radicals
A square root of a number is a value that, when multiplied by itself, gives the original number. The symbol √ denotes the square root. Understanding how to manipulate square roots is essential for simplifying expressions involving radicals.
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Imaginary Roots with the Square Root Property
Multiplication of Radicals
When multiplying two square roots, you can multiply the numbers inside the radicals directly: √a × √b = √(a × b). This property allows simplification of expressions without expanding intermediate steps.
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Simplification of Radical Expressions
Simplifying radicals involves reducing the expression to its simplest form, often by recognizing perfect squares. For example, √6 × √6 equals √(6×6) = √36, which simplifies to 6, a whole number.
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Related Practice
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.
Textbook Question
CONCEPT PREVIEW Evaluate each expression. 3a - 2b, for a = -2 and b = -1
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Textbook Question
CONCEPT PREVIEW Use choices A–D to answer each question.
A. 3x² - 17x - 6 = 0
B.(2x + 5)² = 7
C. x² + x = 12
D. (3x - 1) (x - 7) = 0
Which quadratic equation is set up for direct use of the square root property? Solve it.
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Textbook Question
CONCEPT PREVIEW Rewrite the expression -7(x - 4y) using the distributive property.
Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The circle with equation x² + y² = 49 has center with coordinates ________ and radius equal to _______.
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