Multiple Choice
Rationalize the denominator.
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0. Review of College Algebra
Rationalizing Denominators
2:12 minutesProblem 9
Textbook Question
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps.√6 • √6
Verified step by step guidance1
Recognize that the expression involves multiplying two square roots: \( \sqrt{6} \times \sqrt{6} \).
Recall the property of square roots: \( \sqrt{a} \times \sqrt{a} = a \).
Apply this property to the expression: \( \sqrt{6} \times \sqrt{6} = 6 \).
Understand that this is because the square root and the square are inverse operations.
Conclude that the result of \( \sqrt{6} \times \sqrt{6} \) is simply the number under the square root, which is 6.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Roots
A square root of a number 'x' is a value 'y' such that y² = x. For example, the square root of 6, denoted as √6, is a number that when multiplied by itself gives 6. Understanding square roots is essential for simplifying expressions involving radical signs.
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Multiplication of Square Roots
When multiplying square roots, the product can be simplified using the property √a • √b = √(a • b). This means that the square roots can be combined under a single radical sign, which is crucial for simplifying expressions like √6 • √6.
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Properties of Exponents
The operation of squaring a square root leads to the property that √x • √x = x. This property is fundamental in simplifying expressions involving square roots, as it allows for the direct conversion of the product of square roots back to the original number.
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