What is the Square Root of 288?

The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because 3 x 3 = 9. The square root of 288 can be found by determining which number multiplied by itself equals 288.

What is the Square Root of 288?

The square root of 288 is approximately 16.97 (rounded to two decimal places).

Here’s a table showing the square root of 288 with different levels of precision:

Level of Precision	Square Root of 288
Exact Value	√288
1 Decimal Place	16.97
2 Decimal Places	16.97
3 Decimal Places	16.971
4 Decimal Places	16.9716
5 Decimal Places	16.97159

The exact value of the square root of 288 is represented as √288, and when rounded to various decimal places, it provides approximations for practical use.

To find the square root of 288, we first look at the factors of 288. The factors of 288 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 144, and 288. To find the square root, we are looking for the factor pairs that multiply to give 288. The factor pairs are:

1 x 288 2 x 144 3 x 96 4 x 72 6 x 48 8 x 36 12 x 24 16 x 18

Looking at the factor pairs, we see that 16 x 18 = 288. Therefore, the square root of 288 is 16.

To check this, if we square 16 (multiply 16 x 16), we get 256. This is the closest perfect square less than 288. And if we square 17 (17 x 17), we get 289. This is the closest perfect square greater than 288. So the square root of 288 must lie between 16 and 17. Indeed, 16 is the integer square root of 288.

The precise square root of 288 is 16.6568542. This can be calculated using a calculator or computer program. But when we’re looking for integer square roots, we round down to the nearest integer, which is 16.

Some key properties of square roots:

• The square root of a number times itself equals the original number (√x * √x = x)
• The square root of a positive number is always positive
• The square root of 0 is 0
• There are no real square roots of negative numbers (imaginary numbers like i have square roots)
• Square roots of perfect squares like 4, 9, 16 are integers
• Square roots of other numbers are irrational decimals that go on forever without repeating

Strategies for finding square roots:

• Factoring into factor pairs and looking for the pair that multiplies to the number
• Checking perfect squares smaller and larger to bracket in
• Using a calculator, computer, or square root algorithm
• Estimating / guessing and checking by squaring the guess

The most efficient way to find square roots for large numbers is to use a calculator or computer program. For mental math or doing it by hand, factoring and perfect square strategies tend to work best. Look for patterns and shortcuts like perfect squares (squares of 1, 2, 3, etc.) to estimate roots. With some practice, you can quickly identify square roots or estimate them in your head.

Being able to find square roots is an important mathematical skill with many real world applications. Home and construction projects frequently involve areas and volumes where you need to find square roots. Financial calculations, physics formulas, and statistics also rely heavily on square roots. Mastering square root extraction will give you an edge in algebra, geometry, trigonometry, and even chemistry. It’s a fundamental skill worth developing.

So in summary, the square root of 288 is 16, found by factoring 288 into factor pairs and identifying 16 x 18 as the pair that multiplies to 288. This demonstrates key properties and strategies of square roots. Learning and practicing square root calculation will add a valuable tool to your mathematical skill set. Whether you’re solving math problems by hand or using technology, having a deep understanding of square roots will help you gain mastery over mathematics.