Problem 307 - Elementary Algebra

Question

In the following exercises, simplify. $$ (\sqrt{29})^{2} $$

Step-by-Step Solution

Answer

The simplified form is 29.

Step 1 - Identify the expression

The given expression is \( (\sqrt{29})^2 \).

Step 2 - Understand the square root and square relationship

The square of a square root of a number results in the original number. Mathematically, \( (\sqrt{a})^2 = a \).

Step 3 - Apply the relationship

Using the relationship from Step 2, simplify \( (\sqrt{29})^2 \) to 29.

Key Concepts

headline of the respective core concept

When we're dealing with square roots, it's important to understand how they work and how they simplify. 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 multiplied by 3 is 9.

headline of the respective core concept

Squares are mathematically significant because they pair naturally with square roots. Squaring a number means multiplying it by itself. For example, if you square 4, you multiply 4 by itself, getting 16. Simply put, if you undo a square with a square root or vice versa, you'll get the original number.

headline of the respective core concept

Mathematical relationships often involve recognizing how different operations interact. When you see a square root and a square in an expression, remember that they cancel each other out. Understanding these relationships helps make simplification easier, as shown in our example where \(\sqrt{29}\) squared simply equals 29.