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Understanding how to calculate square roots is essential for many areas of mathematics. The square root of a number is a value that, when multiplied by itself, gives the original number. It's represented by the symbol \( \sqrt{} \). For example, the square root of 9 is 3, because \( 3 \times 3 = 9 \).

To find the square root of a number without a calculator, you would use methods like prime factorization or a long division-like method known as the square root algorithm. However, with the convenience of modern technology, you can simply use a calculator, which saves time and ensures accuracy.

When using a calculator to find the square root of a number, such as \( \sqrt{296} \), you'd input the number 296 and press the square root button. The display will then show the square root, which in this case is a non-integer that goes on indefinitely. Since we rarely need the full decimal expansion, we often round the result, which leads us to our next section.

Rounding decimals is a way to simplify numbers, making them easier to work with, especially for estimations or when a specific level of precision is needed. When you round a number to the hundredths place, you're looking at the third decimal digit to decide whether to round up or down.

To round to the hundredths place:

• Find the third decimal place in the number.
• If this digit is 5 or greater, increase the second decimal place by one and drop all the digits after it.
• If this digit is less than 5, keep the second decimal place the same and drop all the digits after it.

This technique is essential when dealing with financial calculations, measurements, and any time accurate to the hundredths is required without the need for lengthy numbers.

Calculators are a vital tool for performing a wide range of mathematical operations quickly and accurately. To use a calculator effectively, familiarize yourself with its basic functions: addition, subtraction, multiplication, and division, as well as the square root function for more advanced calculations.

For our exercise, pressing the square root key after entering the number 296 gives us the result. Remember to ensure that your calculator is in the correct mode (for example, degree vs. radian for trigonometric calculations) and that you know how to read the display properly, particularly for complex functions. With practice, using a calculator becomes second nature, enabling you to tackle mathematical problems with confidence and ease.