Determining a number such that twice its square root equals 14 is a fun and straightforward mathematical problem. This article will walk you through the process of solving this problem, exploring the basic principles of square roots and equations. By the end, you will fully understand the logic and be able to solve similar problems independently. We will also discuss the significance of these mathematical concepts in real-world applications.

Understanding the Problem

The problem statement is straightforward: we need to find a number x such that twice its square root equals 14. We can formulate this as the equation:

2√x 14

Multiplying and Dividing the Equation

To solve for x, we need to isolate it. Start by dividing both sides of the equation by 2 to simplify:

√x 7

Next, to remove the square root, we square both sides of the equation:

x 72

Calculating the square of 7:

x 49

This means the number we are looking for is 49. To double-check our solution, we can substitute 49 back into the original equation:

2√49 14

Since the square root of 49 is 7, and 2 times 7 is 14, our solution is correct.

Further Explorations

It’s useful to explore a few more examples to solidify our understanding of square roots and their properties:

2×√2 2, √2 1, 12 1 2×√4 4, √4 2, 22 4 2×√9 6, √9 3, 32 9 2×√25 10, √25 5, 52 25 2×√49 14, √49 7, 72 49

Conclusion

We have successfully determined that the number is 49 because twice its square root is indeed 14. This problem showcases how to manipulate equations to solve for unknowns and highlights the importance of understanding square roots, a fundamental concept in mathematics.

Square roots, and more generally, mathematical equations, are crucial in various fields such as engineering, physics, and finance. Mastering these skills is essential for problem-solving in many real-world scenarios. Whether you are a student, a professional, or just curious about mathematics, this problem-solving approach will serve you well.

Find out more about square roots and other mathematical concepts on our website. Thanks for reading, and happy problem-solving!