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Chapter 9: Problem 32

Use a calculator to evaluate each radical. (Objective 1) $$\sqrt{1849}$$

Short Answer

Expert verified
\( \sqrt{1849} = 43 \)

Step by step solution

01

Set up the Radical Expression

The goal is to evaluate the square root of 1849. We write this mathematically as \( \sqrt{1849} \).
02

Use a Calculator

Enter the number 1849 into a calculator and use the square root function \( \sqrt{} \) to find the square root of 1849.
03

Read the Result

After performing the calculation, the calculator should display a result. For \( \sqrt{1849} \), the result displayed should be 43.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Square Root Evaluation
The concept of square root evaluation involves finding a number which, when multiplied by itself, equals the given number. For instance, if you have a number like 1849, and you're trying to find its square root, you're essentially looking for a number that gives 1849 when squared. This process is fundamental in mathematics and is symbolized by the radical sign \( \sqrt{} \). For our original exercise, you are tasked with finding \( \sqrt{1849} \), which tells you the number \( 43 \) works here because \( 43 \times 43 = 1849 \).
  • Finding square roots is widely used in geometry, physics, and engineering.
  • It helps in calculating areas, perimeters, and other physical quantities.
  • Understanding square roots also strengthens problem-solving skills and mathematical reasoning.
It's crucial to get comfortable with the square root evaluation as it forms the basis of many various mathematical calculations.
Using Calculators for Radical Expressions
Let's talk about calculators and how they can simplify radical expressions such as square roots. Modern calculators are equipped with a special button (usually marked as \( \sqrt{} \) or something similar) specifically for calculating square roots. You just need to enter the number and press this button to get the result.
A simple three-step process could be:
  • Input the number, here 1849, into your calculator.
  • Press the square root \( \sqrt{} \) button.
  • Read off the result displayed, which in this case will be 43.
Calculators are designed to handle these operations quickly and accurately, providing a great aid to solve mathematical problems involving radicals. Always have your calculator ready especially when dealing with complex sets of numbers. This tool transforms what might seem like a challenging task into an easy one.
Following Step-by-Step Solutions
Breaking down any problem into step-by-step solutions makes it manageable and less intimidating. With square roots, starting with clarity is key.
For our exercise:
  • Recognize and set up the radical expression \( \sqrt{1849} \).
  • Use your calculator to perform the radical operation by entering 1849 and pressing the square root button.
  • Finally, interpret the result, which should be presented as 43.
This appreciative method guides you systematically through problems and extends beyond just square roots to a wide array of mathematical operations. Learning to follow structured steps not only aids understanding but sharpens your ability to approach and resolve complex problems methodically and efficiently.

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Most popular questions from this chapter

Use a calculator to evaluate each radical. (Objective 1) $$\sqrt{2304}$$

Simplify each expression by using the distributive property. (Objective 2) $$9 \sqrt{3}+4 \sqrt{3}$$

Use a calculator to find a whole number approximation for each expression. $$\sqrt[3]{1456}$$

Find a rational approximation, to the nearest tenth, for each radical expression. (Objective 2) $$4 \sqrt{11}-5 \sqrt{11}-7 \sqrt{11}+2 \sqrt{11}-3 \sqrt{11}$$

Find a rational approximation, to the nearest tenth, for each radical expression. (Objective 2) $$8 \sqrt{7}-4 \sqrt{7}+6 \sqrt{7}$$
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