Square Root Of 200 Simplified

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Introduction

The square root is a fundamental concept in mathematics that represents the value of a number that when multiplied by itself gives the original number. Simplifying the square root of a number involves finding the largest perfect square that divides evenly into the original number. In this article, we will discuss how to simplify the square root of 200 and provide step-by-step solutions for better understanding.

Finding the Factors of 200

To simplify the square root of 200, we first need to find the factors of 200. A factor is a number that divides evenly into another number. The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200.

Identifying Perfect Squares

Next, we need to identify the perfect squares among the factors of 200. A perfect square is a number that is the square of an integer. The perfect squares that divide evenly into 200 are 1, 4, 25, and 100.

Applying the Simplification Formula

To simplify the square root of 200, we can apply the simplification formula, which states that the square root of a product is equal to the product of the square roots of its factors. Using this formula, we can write the square root of 200 as the square root of 100 times the square root of 2. Since the square root of 100 is 10, we can simplify the expression to 10 times the square root of 2.

Alternative Method

Another method to simplify the square root of 200 is to use prime factorization. We can write 200 as the product of its prime factors, which are 2, 2, 2, 5, and 5. Then, we group the prime factors into pairs of two and take one factor from each pair outside the square root. In this case, we have two pairs of 2 and one pair of 5, so we can write the square root of 200 as 2 times 2 times the square root of 5.

Comparing the Methods

Both methods yield the same result, which is 10 times the square root of 2. However, the prime factorization method may be more efficient for larger numbers with many prime factors.

Using a Calculator

If you have a scientific calculator, you can also simplify the square root of 200 by entering the number and pressing the square root button. The result will be a decimal approximation, which is approximately 14.1421.

Real-Life Applications

The concept of square roots and simplification is used in various fields such as engineering, physics, and finance. For example, in construction, engineers use the Pythagorean theorem, which involves finding the square root of the sum of the squares of the sides of a right triangle. In finance, investors use the concept of compound interest, which involves finding the square root of the future value of an investment. Simplifying square roots is essential in making accurate calculations.

Conclusion

Simplifying the square root of 200 involves finding the factors and perfect squares of the number and applying the simplification formula. Alternatively, prime factorization can also be used. The result is 10 times the square root of 2, which can be approximated as 14.1421. The concept of square roots and simplification is used in various fields and is essential in making accurate calculations.