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Chapter 9: Problem 30

Use a calculator to evaluate each radical. (Objective 1) $$\sqrt{9801}$$

Short Answer

Expert verified
The square root of 9801 is 99.

Step by step solution

01

Identifying the Radical

The given exercise asks us to find the square root of the number 9801. The symbol \( \sqrt{} \) denotes the square root, so we need to determine the number which, when multiplied by itself, equals 9801.
02

Using a Calculator

To evaluate \( \sqrt{9801} \) using a calculator, enter 9801, then press the 'square root' (\( \sqrt{} \)) button. This should provide the square root of the number directly.
03

Verify the Result

The calculator should display the result as 99, meaning that 99 multiplied by itself (99 * 99) equals 9801. Verify by computing \( 99^2 \) to ensure that the calculation is correct.

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Key Concepts

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

Understanding the Square Root
The square root of a number refers to a value which, when multiplied by itself, gives the original number. This is indicated using the radical symbol \( \sqrt{} \). In practical terms, finding the square root is essentially asking, "What number multiplied by itself results in my original number?" For example, when asked to determine \( \sqrt{9801} \), it means seeking a number, which when squared (multiplied by itself), equals 9801.
  • It is the reverse operation of squaring a number.
  • The square root has two forms: positive and negative, but in most cases, especially with natural numbers, the positive square root is of interest.
In this exercise, we find that the square root of 9801 is 99 because \( 99 \times 99 = 9801 \). Solving such expressions manually can be lengthy, prompting the use of calculators.
Calculator Usage for Square Roots
Utilizing a calculator to find a square root is straightforward and efficient. Here is a simple guide on how to use it:
  • Input the number whose square root you want to calculate. In this case, type in 9801.
  • Locate the square root button, generally symbolized as \( \sqrt{} \) or "鈭�" on the calculator.
  • Press this button after entering 9801. The device will compute and display the square root.
Using a calculator not only makes the process faster but also reduces the potential of errors from manual calculations. Always ensure your calculator is in the right mode, mostly 'standard' for basic calculations.
Having a reliable calculator is essential in learning and verifying mathematical exercises.
Mathematical Verification of Results
Once a calculation is made using tools like a calculator, it's crucial to verify the outcome, especially in educational settings. Verification ensures understanding and correctness:
  • To verify the square root result of 9801 being 99, multiply 99 by 99.
  • If the operation yields 9801, the calculation is verified to be accurate.
Verification steps like these boost confidence in using calculators and develop deeper comprehension of mathematical concepts.
These steps are particularly helpful in exams or when manually checking transferred knowledge, ensuring that the learning process is not solely reliant on machines. This principle applies to all mathematical problems, not just radical calculations.

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Most popular questions from this chapter

Simplify each expression by using the distributive property. (Objective 2) $$19 \sqrt{5}-8 \sqrt{5}$$

For Problems \(55-70\), rationalize the denominators and simplify. All variables represent positive real numbers. $$ \frac{5}{3 \sqrt{2}-4} $$

Use a calculator to find a rational approximation of each square root. Express your answers to the nearest hundredth. $$\sqrt{98}$$

Evaluate each radical without using a calculator or a table. (Objective 1) $$\sqrt{100}$$

Use a calculator to find a rational approximation of each square root. Express your answers to the nearest hundredth. $$\sqrt{66}$$
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