Problem 38 - Elementary and Intermediate Algebra

Question

Use a calculator to find each square root. Give each answer to four decimal places. See Objective 1. $$ \sqrt{0.0063} $$

Step-by-Step Solution

Answer

The square root of 0.0063 is approximately 0.0794 when rounded to four decimal places.

Step 1: Understanding Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we need to find a number which, when squared, equals 0.0063.

Step 2: Enter the Value

Turn on your calculator and enter the value under the square root symbol, in this case, 0.0063.

Step 3: Calculate the Square Root

Use the square root function on the calculator. On most calculators, this is done by pressing the square root button (often depicted as \( \sqrt{} \)) after entering the number.

Step 4: Record the Answer

The calculator will display the square root of 0.0063. Write this value down, making sure to round the result to four decimal places as specified in the problem statement.

Key Concepts

Calculator Usage

Calculators have become an indispensable tool in studying mathematics, especially when dealing with more complex operations, like finding square roots. With the help of a calculator, you can quickly and accurately perform these computations without the hassle of manual calculations. When using a calculator to find a square root, it's important to familiarize yourself with its basic functions:

• Turn the calculator on and ensure it's in the right mode, usually designated for basic arithmetic.
• Enter the number for which you want to find the square root. In our example, you would input 0.0063.
• Press the square root button, often labeled as \( \sqrt{} \), to calculate the square root.
• Finally, read and interpret the result shown on the display.

Using a calculator not only saves time but also reduces the likelihood of errors, especially when dealing with precision-dependent tasks like this one.

Decimal Places

Rounding numbers to a specific number of decimal places is a crucial skill when dealing with square roots or any other mathematical calculation. Decimal places refer to the number of digits shown to the right of the decimal point. For example, if your calculator displays a square root as 0.079373802, you may need to round this to four decimal places for your final answer: 0.0794. Here's a simple guide to rounding decimal numbers:

• Identify how many decimal places you need. In this case, it is four.
• Look at the fifth decimal place to determine whether to round up or remain. If it's 5 or more, round the fourth place up; if less, keep it the same.
• Modify the number accordingly and ensure all other digits are correct.

Rounding helps maintain uniformity and precision across mathematical computations, allowing clear and direct communication of results.

Mathematical Operations

A foundational understanding of mathematical operations is key to solving problems involving square roots. Square roots fall under the category of exponentiation, where the objective is to find a base number raised to the power of 1/2. In mathematical terms, for a non-negative number \( x \), its square root is represented as \( \sqrt{x} \). This operation asks: "What number, when multiplied by itself, gives \( x \)?"

• To perform the operation manually, consider the number itself and its approximate square roots.
• When using a calculator, it effectively handles these logarithmic processes instantaneously.

Having a solid grasp of these operations aids in understanding the outcome from calculating square roots, reinforcing comprehension and accuracy in mathematical endeavor.