Question

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\sqrt{7}$$

Short answer

2.65

Step-by-step solution

- Understand the Radical

The given expression is the square root of 7, represented as \(\backslash sqrt{7}\). A square root asks for a number which, when multiplied by itself, equals the radicand (in this case, 7).

- Use the Calculator

Enter 7 into the calculator and apply the square root function (√) to get the approximate value. On most calculators, this is done by pressing the √ button.

- Approximate the Result

The calculator will provide the square root of 7, which is approximately 2.6457513110645906. To round this value to two decimal places, check the third decimal place: since it is 5 (which is 5 or more), round up.

- Round the Result

Rounding 2.6457513110645906 to two decimal places results in 2.65.

Key concepts

Calculator Usage

Calculators are essential tools for students, providing quick and accurate results. Basic calculators have functions to perform simple arithmetic operations like addition, subtraction, multiplication, and division. Scientific calculators come with advanced functions such as calculating square roots, trigonometric functions, and logarithms. To approximate a square root using a calculator, follow these steps:

• Turn on the calculator.
• Enter the number you wish to find the square root of, in this case, 7.
• Press the square root (√) button.
• Read the result displayed on the screen.

This method is efficient because it saves time and minimizes errors that might occur when calculating manually. Understanding how to use a calculator properly is crucial for solving math problems accurately.

Rounding Numbers

Rounding numbers makes them simpler to use and understand by reducing the number of digits while keeping them close to the original value. To round a number to a specific decimal place, you need to focus on digits at and just beyond the desired place. Here’s a step-by-step guide to rounding to two decimal places:

• Identify the digit in the third decimal place. In our example of approximating \(\backslash sqrt{7}\) with a starting value of 2.6457513110645906, the third decimal place digit is 5.
• If this digit is 5 or greater, increase the second decimal place by 1. If it is less than 5, keep the second decimal place as it is.
• So, rounding 2.6457513110645906 to two decimal places results in 2.65.

Rounding helps in achieving precision and is especially important when dealing with measurements or financial calculations.

Radicals

Radicals are mathematical expressions involving roots, mainly square roots, cube roots, etc. A square root asks for a number which, when multiplied by itself, equals the original number, called the radicand. For example, \(\backslash sqrt{9}=3\) because \((3 \backslash times 3) = 9\). Here’s how to understand radicals better:

• A square root is just one type of radical, where the index is 2. Other common radicals include cube roots (index 3).
• The radicand is the number inside the radical symbol. In \(\backslash sqrt{7}\), 7 is the radicand.
• Calculating a square root manually involves guessing and checking, or using an algorithm, but a calculator simplifies this process.

Radicals are fundamental in algebra and appear in various areas of mathematics, such as solving equations and simplifying expressions.