Square Root Of 250 Simplified

Square Root of 250 How to Find the Square Root of 250? Cuemath from www.cuemath.com

Introduction

As a professional teacher, it is my responsibility to help my students understand complex mathematical concepts. One such concept is finding the square root of a number. In this article, we will discuss how to simplify the square root of 250.

What is Square Root?

Square root is a mathematical operation that calculates the number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9.

How to Simplify Square Root of 250?

To simplify the square root of 250, we need to find its factors. We can break down 250 into factors of perfect squares to simplify the square root.

Step 1: Prime Factorization

We can start by finding the prime factorization of 250. Prime factorization is the process of breaking down a number into its prime factors. To find the prime factors of 250, we can divide it by the smallest prime number, which is 2. 250 ÷ 2 = 125 125 is not divisible by 2, so we move to the next prime number, which is 3. 125 ÷ 5 = 25 25 ÷ 5 = 5 5 is a prime number, so we stop. Therefore, the prime factorization of 250 is 2 x 5 x 5 x 5.

Step 2: Simplify the Square Root

Now that we have the prime factorization of 250, we can simplify the square root. We can group the factors into pairs of perfect squares, which is a number that can be expressed as the square of an integer. 250 = 2 x 5 x 5 x 5 = 2 x (5 x 5 x 5) = 2 x 5^3 We can simplify the square root of 250 as follows: √250 = √(2 x 5^3) = √2 x √(5^2 x 5) = √2 x 5√5 Therefore, the simplified square root of 250 is 5√2.

Conclusion

Simplifying the square root of 250 requires finding its prime factors and grouping them into pairs of perfect squares. By following the steps outlined above, we can simplify the square root of 250 to 5√2. As a professional teacher, it is important to help students understand complex mathematical concepts such as square roots, as it is a fundamental part of mathematics.