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Chapter 0: Problem 18

Simplify the expression. \(\sqrt{\frac{9}{121}}\)

Short Answer

Expert verified
\frac{3}{11}

Step by step solution

01

Identify components inside the square root

Recognize that the expression inside the square root is \(\frac{9}{121}\).
02

Find the square root of the numerator

The numerator is 9. Find the square root of 9, which is 3, because \(3^2 = 9\).
03

Find the square root of the denominator

The denominator is 121. Find the square root of 121, which is 11, because \(11^2 = 121\).
04

Simplify the expression

Combine the square roots you found from Steps 2 and 3 to get \(\frac{3}{11}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Square Roots
Square roots are an essential concept in algebra, frequently encountered when simplifying expressions.
The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 9 is 3 because \(3^2 = 9\).
In mathematical notation, the square root of a number is often represented by the radical symbol \( \sqrt{} \).
Here are a few more examples to illustrate square roots:
  • The square root of 16 is 4 because \(4^2 = 16\)
  • The square root of 25 is 5 because \(5^2 = 25 \)
  • The square root of 36 is 6 because \(6^2 = 36 \)
Remember, not all numbers have a whole number as their square root. For instance, the square root of 2 is an irrational number approximately equal to 1.414.
Numerator and Denominator
In fractions, understanding numerators and denominators is crucial.
A fraction is composed of two parts: the numerator and the denominator. The numerator is the top number and indicates how many parts are being considered. The denominator is the bottom number, representing the total number of equal parts.
For example, in the fraction \(\frac{3}{4}\),
  • 3 is the numerator, showing that three parts are considered
  • 4 is the denominator, indicating that the whole is divided into four equal parts
Properly understanding and identifying these components aids in various algebraic operations, such as simplification, addition, subtraction, multiplication, and division of fractions.
Fraction Simplification
Simplifying fractions is an important skill in algebra.
It involves reducing the fraction to its simplest form, where the numerator and denominator share no common factors other than 1.
To simplify a fraction, follow these steps:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
For example, to simplify \( \frac{18}{24} \):
  • The GCD of 18 and 24 is 6.
  • Divide both the numerator and the denominator by 6.
  • The simplified fraction is \(\frac{3}{4}\).
This process helps in making calculations easier and results more understandable.

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Most popular questions from this chapter

If \(n<0,\) then \(n+|n|=\) _____ .

Add or subtract as indicated and simplify. $$ \text { Subtract }\left(\frac{1}{2} x^{2}-\frac{3}{4} x-\sqrt{2}\right) \text { from }\left(\frac{1}{4} x^{2}+\frac{5}{8} x+5 \sqrt{2}\right) $$

Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ (\sqrt{y+2}-4)^{2} $$

Multiply and simplify. $$ \left(-10 c^{2} d^{5}\right)\left(\frac{1}{2} c d^{7}\right) $$

Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ 3 \sqrt{6}(5 \sqrt{3}-4 \sqrt{2}-\sqrt{6}) $$
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