Simplify the following radical expression. Do not leave decimals or [tex]$\sqrt{ }$[/tex] in the denominator.
[tex]
\begin{array}{l}
\sqrt{44} \\
44_{13}=2=2=11
\end{array}
[/tex]
Answer (1)
Find the prime factorization of 44: 44 = 2 2 × 11 .
Rewrite the square root: 44 = 2 2 × 11 .
Use the property of square roots: 2 2 × 11 = 2 2 × 11 .
Simplify: 2 11 .
2 11
Explanation
Understanding the problem We are asked to simplify the radical expression 44 . This means we want to find the largest perfect square that divides 44 and then simplify the radical.
Prime factorization First, we find the prime factorization of 44. We have 44 = 2 × 22 = 2 × 2 × 11 = 2 2 × 11 .
Using properties of square roots Now we can rewrite the square root as 44 = 2 2 × 11 . Using the property that a × b = a × b , we have 2 2 × 11 = 2 2 × 11 .
Simplifying the expression Since 2 2 = 2 , we can simplify the expression to 2 11 . This is the simplified form of 44 .
Final Answer Therefore, the simplified form of 44 is 2 11 .
Examples
Radical expressions are used in many areas of mathematics and physics. For example, when calculating the distance between two points in a coordinate plane, we often encounter square roots. Simplifying these radicals helps us to express the distances in a more understandable and manageable form. Another example is in physics, when calculating the period of a pendulum, which involves a square root. Simplifying the radical makes it easier to understand the relationship between the length of the pendulum and its period.
