Problem 35 - Elementary and Intermediate Algebra

Question

Use a calculator to find each square root. Give each answer to four decimal places. See Objective 1. $$ \sqrt{12} $$

Step-by-Step Solution

Answer

The square root of 12 is approximately 3.4641.

Step 1: Understand the Problem

The problem is asking to compute the square root of 12 and express the answer rounded to four decimal places. The square root of a number \( n \) is a value that, when multiplied by itself, gives \( n \).

Step 2: Use a Calculator

Use a calculator to compute the square root of 12. Enter 12 into the calculator and then press the square root function. The calculator will display the square root of 12.

Step 3: Round the Result

The calculator will give a decimal number as the square root of 12. Round this decimal to four decimal places to get the final answer.

Key Concepts

Using a Calculator

Calculators are incredibly handy tools for performing complex mathematical operations quickly and accurately. When you want to find the square root of a number like 12, a calculator simplifies this task. First, ensure that your calculator is switched on and ready to be used. Most calculators have a specific button for square roots, often denoted as a small square root symbol (√). To find the square root of 12, start by entering the number 12 into your calculator. Then, press the square root button. Your calculator should instantly compute the square root and display a long decimal answer, which represents the exact square root of 12. Using a calculator for this operation saves you from doing paper-and-pencil approximations, which might be time-consuming and prone to error. Always check your calculator's manual if you're unsure where the square root button is or how to activate it. Many modern calculators, including those on smartphones, have touchscreen interfaces where you can simply tap the required buttons.

Rounding Decimals

Once you've got the square root of 12 from your calculator, you need to round it to four decimal places. This means you'll turn a long string of numbers into a more manageable form without losing much accuracy. Rounding determines which decimal places are significant enough to keep. For example, if your calculator gives you a square root of 3.464101615, you'll round it to 3.4641. To do this, look at the fifth decimal place, which in this case is a 0. If this number were 5 or more, you'd round the fourth decimal place up by one. Since it's less than 5, you leave the fourth digit as is. Here's a quick guide:

• Identify the fifth decimal digit.
• If the fifth digit is 5 or greater, increase the fourth digit by one.
• If the fifth digit is less than 5, keep the fourth digit the same.

This process of rounding helps make numbers easier to read and work with, especially when precision beyond a certain point is unnecessary.

Mathematical Operations

In mathematics, operations are procedures or actions that are carried out on numbers. These include addition, subtraction, multiplication, division, and finding roots like squares and cube roots.Square roots fall under more complex operations but are important as they undo the square of a number. The operation can be symbolized by placing a number under a square root sign (√), indicating the number from which you want to find the square root.For instance, to `square` a number is to multiply it by itself: \[ x^2 = x \times x \]Conversely, the square root operation asks: "What number multiplied by itself gives the original number?" This is challenging without calculators for non-perfect squares like 12.Modern calculators handle these complex operations with ease, and understanding how to use them effectively can significantly reduce computation time and error. Remember that mathematical operations are the building blocks of all calculations and learning how to handle them with tools like calculators is greatly beneficial. They don't just solve for exact solutions but also help to verify your manual calculations if needed.