Simplifying Square Root Of 245: Explanation And Solution

Find the square root of 245 correct to 2 decimal places Brainly.in from brainly.in

Introduction

Square roots are an essential part of mathematics, and understanding how to simplify them is crucial for solving complex mathematical problems. In this article, we will discuss how to simplify the square root of 245 and provide a step-by-step solution.

What is a Square Root?

A square root is the inverse operation of squaring a number. It 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.

Simplifying Square Roots

To simplify a square root, we need to find the factors of the number inside the radical sign. In the case of 245, we can break it down into its prime factors: 245 = 5 x 7 x 7 Now, we can rewrite the square root of 245 as the product of the square root of the factors: √245 = √(5 x 7 x 7) = √5 x √7 x √7 = √5 x 7

Final Solution

Therefore, the simplified form of the square root of 245 is √5 x 7.

Step-by-Step Solution

1. Write the number inside the radical sign as the product of its prime factors: 245 = 5 x 7 x 7 2. Group the factors into pairs of two: 245 = (5 x 7) x 7 3. Take the square root of each pair: 245 = √(5 x 7) x √7 4. Simplify the square root of each pair: 245 = √35 x √7 5. Multiply the square roots together: 245 = √5 x 7

Practice Problems

Now that we have learned how to simplify square roots, let's try some practice problems: 1. Simplify the square root of 180: 180 = 2 x 2 x 3 x 3 x 5 = 2 x 3 x 3 x √5 = 6√5 Answer: 6√5 2. Simplify the square root of 252: 252 = 2 x 2 x 3 x 3 x 7 = 2 x 3 x 3 x √7 = 6√7 Answer: 6√7

Conclusion

Simplifying square roots is an important skill to have in mathematics. By breaking down the number into its prime factors and grouping them into pairs, we can simplify the square root and make it easier to work with. Remember to always check your work and simplify the square root as much as possible.