Problem 79 - Fundamentals of Mathematics

Question

Use a calculator with the keys \(\sqrt{x}, y^{x}\), and \(1 / x\) to find each of the values. \(\sqrt{1,156}\)

Step-by-Step Solution

Answer

The square root of 1,156 is 34.

Step 1: Understand the Problem

We need to find the square root of 1,156, which is written as \(\sqrt{1,156}\). The calculator will help calculate the exact value.

Step 2: Use the Square Root Key

Turn on your calculator. Locate the square root key, usually represented as \(\sqrt{x}\).

Step 3: Enter the Value

Type 1156 into the calculator after pressing the square root key or simply press the square root key and then enter 1156 (this depends on the calculator used).

Step 4: Compute the Result

Press the equal sign (usually represented as \(=\)) or the enter key to compute the result.

Step 5: Result Verification

Verify the result on the calculator display. The screen should show the square root value.

Step 6: Interpret the Answer

The calculator will show 34 as the result, which is \(\sqrt{1,156}\). Therefore, \(\sqrt{1,156} = 34\).

Key Concepts

Square Root Calculation

Understanding square roots is essential when it comes to finding a number that, when multiplied by itself, equals the given value. In this case, we're calculating the square root of 1,156. The square root symbol is represented as \(\sqrt{\cdot}\). So, \(\sqrt{1,156}\) is the value we need to find.

When determining a square root by hand, one would typically use prime factorization or estimation techniques, but let's simplify things by using a calculator. Calculators are equipped to handle this calculation accurately and swiftly, showing us the result without any manual steps. This is beneficial especially when dealing with larger numbers or when precision is necessary.

Step by Step Problem Solving

Solving problems step by step allows us to break down what might initially seem complex into manageable parts. In this particular exercise, finding \(\sqrt{1,156}\) is more approachable when we follow a structured approach.

• Understand the problem: Identify what you're trying to solve. Here, it is the square root of 1,156.
• Use the calculator effectively: Identify the correct keys, such as the square root key \(\sqrt{x}\).
• Enter the number: Input 1,156 correctly.
• Compute and verify: Press the equal sign to see the result, and ensure it aligns with expectations.
• Interpret the result: Recognize the answer. For our example, \(\sqrt{1,156} = 34\).

Each step plays a vital role in ensuring that the calculation is performed correctly and efficiently. Following these steps also helps minimize errors, making problem-solving clearer and more reliable.

Calculator Functions

Calculators offer various functions that make mathematical calculations more straightforward. By leveraging special keys tailored for specific operations, such exercises become hassle-free.

The primary function here is the square root \(\sqrt{x}\) key, which simplifies finding the root of numbers. Using this function requires just a few button presses, showcasing how calculators have transformed mathematical computations. Additionally, functions like \(y^{x}\) for exponentiation and \(1/x\) for reciprocals can further enhance our ability to solve complex expressions easily.

• Square Root Key: This automatically calculates the square root when the number is inputted.
• Efficiency: Saves time, especially with larger numbers or repeated calculations.
• Accuracy: Minimizes human error by providing precise numerical outputs.

Utilizing these functions not only streamlines the problem-solving process but also builds confidence in handling a variety of mathematical challenges with ease.