When dealing with algebraic expressions, especially those involving square roots, it is often essential to break down the problem into clear, step-by-step steps. Today, we will dissect a straightforward but interesting mathematical problem: 'Is the square root of a number increased by 3 equal to 8?' This type of question is quite common in algebraic problem-solving scenarios.

Problem Statement

Let's begin with the statement: √x - 3 8. This can be rearranged to √x 8 3. Therefore, √x 11. To find the value of x, we need to square both sides of the equation: x 11^2 121.

Simplified Solution 1

To break down this problem, let’s consider the following steps:

Identify the equation: Let the number be x. The problem can be written as √x - 3 8. Solve for the square root: Add 3 to both sides to isolate the square root: √x 11. Solve for x: Square both sides to eliminate the square root: x 11^2 121.

Simplified Solution 2

Alternatively, let’s use another approach to solve the problem:

Identify the equation: Let the number be x. The problem can be written as √x - 3 8. Solve for the square root: Add 3 to both sides to isolate the square root: √x 8 3. Therefore, √x 11. Solve for x: Square both sides to eliminate the square root: x 11^2 121.

Interpreting the Problem

The question at hand can be approached in multiple ways. Given the equation:

√x - 3 8

Adding 3 to both sides:

√x 11

Squaring both sides:

x 11^2 121

This method ensures that the value of x is correctly determined.

Conclusion

In summary, when faced with a problem involving the square root of a number increased by a certain value, it is crucial to isolate the square root term, solve it, and then square both sides to find the value of the original number. This problem demonstrates the importance of step-by-step logical reasoning in algebraic problem-solving. Whether you are a student, a professional, or simply someone who enjoys solving puzzles, you can apply this method to solve similar problems effectively.