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Chapter 5: Problem 79

Use a calculator to approximate the square root to the nearest tenth. \(\sqrt{615}\)

Short Answer

Expert verified
The approximate value of \( \sqrt{615} \) to the nearest tenth is 24.8.

Step by step solution

01

Identify the task

We need to approximate the value of the square root of 615, that is, \( \sqrt{615} \), to the nearest tenth using a calculator.
02

Use a calculator

Enter 615 into your calculator and apply the square root function. This is typically represented by a button with the symbol \( \sqrt{} \).
03

Read the calculator result

After performing the calculation, the calculator should display a value close to 24.799.
04

Round to the nearest tenth

Look at the first decimal place of the result: 24.799. Since the hundredths digit is 9, we round the tenths place up from 7 to 8.

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Key Concepts

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

Calculator Use
Calculators are essential tools for performing complex mathematical operations efficiently, especially when dealing with square roots. When you want to approximate a square root like \(\sqrt{615}\), you can use a calculator to do so easily. Start by locating the square root button, which is often represented by the symbol \(\sqrt{}\). Enter the number you need the square root of, which in this case is 615. After pressing the square root button, your calculator will provide an exact or very close approximation of the square root.
  • This process helps save time and ensures accuracy in calculations.
  • Always make sure your calculator is in the correct mode and functioning properly.
  • Double-check that you've pressed the right buttons to avoid any errors.
Rounding Decimals
Rounding decimals is an important skill that simplifies numbers, making them easier to work with or understand. When rounding a number to the nearest tenth, we focus on the digit in the tenths place and the digit immediately after it (the hundredths place). For \(24.799\), observe the hundredths place, which is 9. The rule is simple:If the digit in the hundredths position is 5 or higher, round up. If it's less than 5, round down. Since 9 is greater than 5, you would round up the tenths digit from 7 to 8, resulting in 24.8. This small adjustment simplifies data without drastically affecting accuracy.
  • Rounding allows for cleaner numbers, making data easier to read.
  • Keep in mind that rounding can introduce minor errors, so always use it judiciously.
Approximating Values
Approximating values is a handy mathematical skill that provides estimated results when exact answers are unnecessary or difficult to obtain. This technique involves finding a number that is close enough to the true value for practical purposes. When finding \(\sqrt{615}\), using a calculator's precision gives us 24.799. But for practical purposes, this number might need to be rounded or approximated to 24.8.Approximations are particularly useful when dealing with:
  • Measurements in daily activities like cooking or shopping.
  • Engineering tasks where precision can be too cumbersome.
  • Financial calculations where rough estimates are necessary for budgeting.
Using these techniques efficiently can save time and make calculations feasible in real-life scenarios.

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Most popular questions from this chapter

Simplify the given expression. \(\frac{1.5(-8.8)-(-18.6)}{1.8}\)

Divide the decimals. \(\frac{0.3901}{0.83}\)

Compute the exact square root. \(\sqrt{\frac{49}{36}}\)

Multiply the decimals. (21.4)(0.6)

Your solutions should include a well-labeled sketch. The length of one leg of a right triangle is 4 meters, and the length of the hypotenuse is 12 meters. Find the length of the other leg. Round your answer to the nearest hundredth.
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