Simplifying 48 To Simplest Radical Form

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Simplifying 48 To Simplest Radical Form

When it comes to working with radicals, one of the most important skills to master is simplifying them to their simplest form. This involves expressing the radical in a way that minimizes the number under the radical sign, making it easier to work with. In this article, we'll explore the process of simplifying the square root of 48 to its simplest radical form.

Radicals, also known as roots, are mathematical expressions that represent a number that, when multiplied by itself, gives a specified value. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. Radicals are denoted by the radical sign, √, and are commonly used in algebra, geometry, and other branches of mathematics.

What is the Square Root of 48?

To simplify the square root of 48, we need to find the largest perfect square that divides evenly into 48. A perfect square is a number that can be expressed as the square of an integer. For example, 16 is a perfect square because it is the square of 4.

To simplify the square root of 48, we can start by factoring the number under the radical sign. 48 can be factored as 16 × 3, since 16 is a perfect square and 3 is a prime number.

Factoring the Number Under the Radical Sign

• 48 = 16 × 3
• √48 = √(16 × 3)

Now, we can simplify the radical by pulling out the perfect square factor:

• √(16 × 3) = √16 × √3
• √16 = 4, since 4 multiplied by 4 equals 16

So, the simplified form of the square root of 48 is:

• √48 = 4√3

Working with Simplified Radicals

Now that we have simplified the square root of 48 to its simplest radical form, we can use this expression to simplify other mathematical expressions. For example, if we have an expression that involves the square root of 48, we can substitute the simplified form into the expression.

For example, suppose we have the expression:

• 2√48 + 3

We can substitute the simplified form of the square root of 48 into the expression:

• 2(4√3) + 3
• 8√3 + 3

By simplifying the radical, we have made it easier to work with the expression.

Practical Applications of Simplified Radicals

Simplified radicals have many practical applications in mathematics, science, and engineering. For example, in geometry, radicals are used to calculate the lengths of sides and diagonals of triangles and quadrilaterals. In physics, radicals are used to calculate the magnitude of forces and velocities.

In engineering, radicals are used to calculate the stresses and strains on materials. For example, in civil engineering, radicals are used to calculate the loads on bridges and buildings.

By simplifying radicals, we can make it easier to work with these expressions and apply them to real-world problems.

Examples of Practical Applications

• Calculating the length of a side of a triangle using the Pythagorean theorem
• Calculating the magnitude of a force using Newton's laws of motion
• Calculating the stress on a material using the formulas of mechanics

By mastering the skill of simplifying radicals, we can make it easier to work with these expressions and apply them to a wide range of practical problems.

Conclusion

In conclusion, simplifying radicals is an important skill to master in mathematics. By simplifying the square root of 48 to its simplest radical form, we can make it easier to work with this expression and apply it to a wide range of practical problems.

We hope this article has helped you understand the process of simplifying radicals and has given you a deeper appreciation for the importance of this skill. If you have any questions or comments, please feel free to share them with us.