Simplifying The Square Root Of 175

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Introduction

As a professional teacher, one of the most important skills that I teach my students is simplifying square roots. Simplifying square roots is a fundamental concept in mathematics that helps students to solve complex equations and problems. In this article, I will explain how to simplify the square root of 175 step by step.

What is a Square Root?

A square root is a value 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. The symbol for square root is √.

What is the Square Root of 175?

Finding the exact square root of 175 is not possible because 175 is not a perfect square. However, we can simplify the square root of 175 to make it easier to work with.

Step-by-Step Guide to Simplifying the Square Root of 175

Step 1: Find the prime factorization of 175. To find the prime factorization of 175, we need to divide it by the smallest prime number, which is 2. 175 ÷ 2 = 87.5 Since 87.5 is not a whole number, we need to try the next prime number, which is 3. 175 ÷ 3 = 58.33 Again, 58.33 is not a whole number. We need to try the next prime number, which is 5. 175 ÷ 5 = 35 35 is a whole number, so we can stop dividing. The prime factorization of 175 is 5 × 5 × 7. Step 2: Rewrite the square root of 175 using the prime factorization. √175 = √(5 × 5 × 7) Step 3: Simplify the square root using the product property of square roots. √(5 × 5 × 7) = √5 × √5 × √7 Step 4: Combine the like terms. √5 × √5 × √7 = 5√7

Conclusion

In conclusion, simplifying the square root of 175 requires finding the prime factorization of 175 and using the product property of square roots to simplify the expression. By following the step-by-step guide outlined in this article, students can easily simplify square roots and solve complex equations.