Problem 33 - Algebra 1: Concepts and Skills

Question

Simplify the expression. $$ \sqrt{\frac{4}{16}} $$

Step-by-Step Solution

Answer

The simplified expression is 0.5.

Step 1: Perform the Division

The division in the fraction, \(\frac{4}{16}\), gives the result 0.25.

Step 2: Perform the Square Root

Next, the square root of 0.25 must be calculated. The square root of 0.25 is 0.5.

Key Concepts

Square Root

Understanding the square root is crucial to solving many math problems. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 equals 9. In our exercise, after simplifying the fraction to 0.25, we need to find the square root of 0.25.
The square root of a decimal can be less straightforward but follows the same logic. For 0.25:

• Think of 0.25 as a square: if 0.5 is the side length of a square, then its area would be 0.25, because 0.5 x 0.5 equals 0.25.

Taking the square root of 0.25, we find that it equals 0.5. Understanding this concept is important as it allows you to simplify more complex problems involving square roots.

Fractions

Fractions represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). In the fraction \(\frac{4}{16}\), 4 is the numerator and 16 is the denominator. Simplifying fractions often involves division to make calculations easier.
To simplify, check if both numbers can be divided by the same number. This is called finding the "common factor." In our example:

• Both 4 and 16 are divisible by 4.
• When you divide both by 4, \(\frac{4}{16}\) simplifies to \(\frac{1}{4}\).

Understanding fractions and simplification allows you to see numbers more clearly and work faster in mathematics.

Division

Division is crucial in breaking down numbers into simpler forms. It is essentially the opposite of multiplication. The fraction \(\frac{4}{16}\) can be read as dividing 4 by 16. By performing this calculation, you aim to simplify the fraction.

• To simplify \(\frac{4}{16}\), perform the division: 4 divided by 16 equals 0.25.

This simplified decimal form allows for easier calculation when finding roots or performing other operations. Division helps you transform expressions into simpler decimal forms, which are often easier to understand and use in further calculations.