Understanding And Solving 8√3

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Introduction

The square root (√) symbol is used to represent the number that when multiplied by itself, gives the original number. For example, √4 = 2 because 2 x 2 = 4. In this article, we will focus on √3 and how to solve 8√3.

What is √3?

√3 is an irrational number, meaning it cannot be expressed as a fraction and its decimal representation goes on infinitely without repeating. It is approximately equal to 1.732.

What is 8√3?

8√3 simply means 8 multiplied by the square root of 3. It is important to note that the square root symbol only applies to the number 3, not 8. Therefore, 8√3 cannot be simplified any further.

When is 8√3 used?

In mathematics, 8√3 is commonly used in geometry to calculate the length of the diagonal of a square with sides of length 4.

How to Calculate 8√3

To calculate 8√3, we simply multiply 8 by the square root of 3. Using a calculator, we get: 8 x √3 = 8 x 1.732 = 13.856 Therefore, 8√3 is approximately equal to 13.856.

Real-Life Applications

Aside from geometry, 8√3 can also be found in real-life applications such as in the construction industry. For example, if a builder needs to calculate the length of a diagonal brace for a rectangular structure with sides of length 8 and 10, they can use the formula: Diagonal brace = √(8^2 + 10^2) Simplifying the formula, we get: Diagonal brace = √(64 + 100) = √164 Multiplying by 8, we get: 8√164 = 8 x 12.806 = 102.448 Therefore, the length of the diagonal brace is approximately equal to 102.448.

Common Mistakes

One common mistake when dealing with square roots is forgetting to simplify the number inside the square root before multiplying. For example, in the formula for the diagonal brace above, some people may forget to simplify 8^2 and 10^2 before adding them together.

Conclusion

In conclusion, 8√3 is a mathematical expression that cannot be simplified further. It is commonly used in geometry to calculate the length of the diagonal of a square with sides of length 4. It can also be found in real-life applications such as in the construction industry. Remember to simplify the number inside the square root before multiplying to avoid common mistakes.