In Exercises 83–90, evaluate each expression without using a calculator. 36^(1/2)

Verified step by step guidance

1. Recognize that the expression \(36^{1/2}\) is asking for the square root of 36.
2. Recall that the square root of a number \(x\) is a value \(y\) such that \(y^2 = x\).
3. Identify the number whose square is 36. In this case, think of numbers that multiply by themselves to give 36.
4. Consider the positive and negative roots, but focus on the principal (positive) square root for this exercise.
5. Conclude that the principal square root of 36 is the number that, when squared, equals 36.

Key Concepts

Exponents

Exponents are a mathematical notation indicating the number of times a number, known as the base, is multiplied by itself. In the expression 36^(1/2), the exponent 1/2 signifies the square root of the base, which is 36. Understanding exponents is crucial for simplifying expressions and performing operations involving powers and roots.

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 36 is 6, since 6 * 6 = 36. Recognizing how to compute square roots is essential for evaluating expressions involving fractional exponents, particularly those with a denominator of 2.

Radical Notation

Radical notation is a way to express roots using the radical symbol (√). The expression 36^(1/2) can also be written as √36. Understanding radical notation helps in recognizing and simplifying expressions involving roots, making it easier to evaluate them without a calculator.