Square Root Of 300 Simplified: Explanation And Solution

Square Root of 300 How to Find the Square Root of 300? from www.cuemath.com

Introduction

Calculating the square root of a number is one of the fundamental operations in mathematics. However, finding the square root of a large number can be a bit tricky, especially if the number is not a perfect square. In this article, we will discuss how to simplify the square root of 300 and provide an easy solution.

What is Square Root?

The square root of a number is the value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 x 3 = 9. The symbol used to represent square root is √.

Is 300 a Perfect Square?

A perfect square is a number that has an integer square root. For example, 9, 16, and 25 are perfect squares because their square roots are integers: 3, 4, and 5 respectively. However, 300 is not a perfect square because its square root is not an integer.

How to Simplify the Square Root of 300?

To simplify the square root of 300, we need to factor it into its prime factors. The prime factorization of 300 is 2 x 2 x 3 x 5 x 5. We can then group the prime factors into pairs of two to simplify the expression.

Step 1: Group the Prime Factors

We can group the prime factors of 300 as follows: √(2 x 2 x 3 x 5 x 5) = √[(2 x 2) x (3 x 5 x 5)]

Step 2: Simplify the Expression

We can simplify the expression by taking the square root of the perfect squares inside the square root: √[(2 x 2) x (3 x 5 x 5)] = √(2 x 2) x √(3 x 5 x 5) = 2√(3 x 5 x 5)

Final Answer

Therefore, the simplified form of the square root of 300 is 2√(3 x 5 x 5), which can also be written as 10√3.

Conclusion

In conclusion, simplifying the square root of 300 requires factoring the number into its prime factors and grouping them into pairs of two. We can then simplify the expression by taking the square root of the perfect squares inside the square root. The final answer is 10√3.