In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25

Verified step by step guidance

1. Identify the expression to evaluate: \( \sqrt{\frac{1}{25}} \).
2. Recognize that the expression involves finding the square root of a fraction.
3. Recall the property of square roots: \( \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} \).
4. Apply this property to the expression: \( \sqrt{\frac{1}{25}} = \frac{\sqrt{1}}{\sqrt{25}} \).
5. Evaluate the square roots: \( \sqrt{1} = 1 \) and \( \sqrt{25} = 5 \), then simplify the fraction.

Key Concepts

Square Roots

The square root of a number 'x' is a value 'y' such that y² = x. In this context, we are evaluating the square root of a fraction, which can be simplified by taking the square root of the numerator and the denominator separately. Understanding how to compute square roots is essential for evaluating expressions involving radical signs.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. The expression √(1/25) involves a rational number, and recognizing that both 1 and 25 are integers helps in determining that the square root will also yield a rational result. This concept is crucial for identifying whether the result of an expression is a real number.

Real Numbers

Real numbers include all the rational and irrational numbers, encompassing integers, fractions, and decimals. When evaluating expressions, it is important to determine if the result is a real number. In this case, since the square root of a positive rational number is also a real number, understanding this classification helps in concluding the evaluation of the expression.