In mathematics, square roots are important as they help us to determine the value of a number when multiplied by itself. The square root of a number is represented by the symbol √. Simplified square roots are those that are reduced to their simplest form. In this article, we will discuss the simplified square root of 6.
What is Square Root?
A square root is a number that, when multiplied by itself, equals the original number. For example, the square root of 25 is 5 because 5 multiplied by 5 equals 25. The square root of 6 is an irrational number, which means it cannot be expressed as a simple fraction. The value of the square root of 6 is approximately 2.45.
How to Simplify Square Root of 6?
To simplify the square root of 6, we need to find the factors of 6 that are perfect squares. The perfect squares that are factors of 6 are 1, 4, and 9. Therefore, we can write the square root of 6 as √(2x3), which can be further simplified as √2 x √3. Hence, the simplified square root of 6 is √6 = √2 x √3.
Why is Simplifying Square Roots Important?
Simplifying square roots is important because it helps us to perform mathematical operations more easily. Simplified square roots make it easier to multiply and divide numbers that involve square roots. They also help us to compare and order numbers that involve square roots.
Examples of Simplified Square Root of 6
Example 1: Simplify √(24) Solution: We can write 24 as 2 x 12 or 4 x 6. Since 6 is a factor of 24, we can simplify it as √(4x6). Therefore, √(24) = √4 x √6 = 2√6. Example 2: Simplify √(54) Solution: We can write 54 as 6 x 9 or 3 x 18 or 2 x 27. Since 6 is a factor of 54, we can simplify it as √(6x9). Therefore, √(54) = √6 x √9 = 3√6.
Conclusion
In conclusion, the simplified square root of 6 is √2 x √3. We can simplify square roots by finding the perfect square factors of a number. Simplified square roots make it easier to perform mathematical operations and compare numbers.
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