Problem 16 - Prealgebra

Question

Use a calculator to find each square root to the nearest tenth. $$\sqrt{56}$$

Step-by-Step Solution

Answer

The square root of 56 is approximately 7.5.

Step 1: Understanding the Square Root

To find the square root of 56, we are looking for a number which, when multiplied by itself, will give us 56. The square root symbol, \(\sqrt{}\), denotes this operation.

Step 2: Using a Calculator

Enter 56 into your calculator and press the square root function (often represented by a button labeled \(\sqrt{}\)). The display will show the square root as an approximate decimal value.

Step 3: Rounding to the Nearest Tenth

The calculator will likely display several decimal places after the square root calculation. Identify the tenths place (the first digit to the right of the decimal point) and round this number based on the digit in the hundredths place. If the hundredths digit is 5 or greater, round up. Otherwise, maintain the current tenths value.

Key Concepts

Calculator Use

Using a calculator to find the square root of a number is easy and saves time. Modern calculators have a special function just for square roots. Look for a button labeled with the square root symbol, \(\sqrt{}\). Here's how you can use it:

• First, make sure your calculator is turned on.
• Enter the number you want to find the square root of, in this case, 56.
• Press the square root button. The calculator will display the square root of the number you entered.

This process will give you a decimal number, which is an approximation of the actual square root.

Rounding Decimals

When you find a square root with a calculator, it often shows many decimal places. But most of the time, you only need an answer rounded to one decimal place, or to the nearest tenth.
To round to the nearest tenth:

• Locate the tenths place. This is the first digit to the right of the decimal point.
• Look at the digit to the right of the tenths place, in the hundredths spot.
• If the hundredths digit is 5 or more, increase the tenths digit by one.
• If it's less than 5, keep the tenths digit the same.

This simple method helps in presenting your answer in a more concise way.

Mathematical Symbols

Mathematical symbols are like a universal language used to express operations and numbers. The square root symbol, \(\sqrt{}\), is one of these. It tells you to find a number that, when multiplied by itself, equals the number under the symbol.
Other key symbols include:

• Addition: plus sign \(+\)
• Subtraction: minus sign \(-\)
• Multiplication: times sign \(\times\) or \(\cdot\)
• Division: division sign \(\div\) or slash \(/\)

Each symbol has a specific meaning and function, which helps simplify and solve math problems efficiently.

Number Operations

Number operations involve different ways of combining or manipulating numbers. Finding a square root is just one operation. Here's a brief look at some basic ones:

• Addition: Combining two or more numbers to find a sum.
• Subtraction: Finding the difference between numbers.
• Multiplication: Adding a number to itself a certain number of times.
• Division: Splitting a number into equal parts.

Square root is the inverse operation of squaring a number. If \(x^2 = y\), then \(\sqrt{y} = x\). Understanding these concepts helps in solving more complex mathematical problems.