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Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblem 83
Chapter 1, Problem 83

Evaluate each expression without using a calculator. 361/2

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1
Recognize that the expression \(36^{\frac{1}{2}}\) represents the square root of 36 because an exponent of \(\frac{1}{2}\) is equivalent to taking the square root.
Rewrite the expression using the square root notation: \(\sqrt{36}\).
Recall that the square root of a number is a value that, when multiplied by itself, gives the original number.
Identify the number which, when squared, equals 36. Since \(6 \times 6 = 36\), the square root of 36 is 6.
Therefore, \(36^{\frac{1}{2}} = \sqrt{36} = 6\).

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Key Concepts

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

Exponents and Radicals

Exponents represent repeated multiplication, and fractional exponents indicate roots. For example, a^(1/2) means the square root of a. Understanding how to interpret and manipulate fractional exponents is essential for evaluating expressions like 36^(1/2).
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Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 36 is 6 because 6 × 6 = 36. Recognizing perfect squares helps simplify expressions without a calculator.
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Simplification of Expressions

Simplifying expressions involves rewriting them in a simpler or more understandable form. This includes breaking down numbers into their prime factors or perfect squares to evaluate roots or powers easily, which is crucial when calculators are not allowed.
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