Simplifying Square Root Of 30

simplifying square root worksheets from printablecampuspiers.z21.web.core.windows.net

Introduction

As a teacher, simplifying square roots is a common topic in mathematics. One such problem is simplifying the square root of 30. This problem can be solved by following a specific set of rules and steps. In this article, we will discuss the steps to simplify the square root of 30.

What is Square Root?

A square root is a number that when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 multiplied by 2 is 4. In the case of the square root of 30, we are looking for a number that when multiplied by itself equals 30.

Simplifying Square Root of 30

To simplify the square root of 30, we must first factor the number 30 into its prime factors. We can do this by dividing 30 by the smallest prime number, 2. The result is 15. We can continue dividing 15 by 2 until we cannot divide any further. The prime factors of 30 are 2, 3, and 5.

Step-by-Step Guide to Simplify Square Root of 30

Step 1: Factorize the number 30 into its prime factors, which are 2, 3, and 5.

Step 2: Take out any pairs of the same prime factors and multiply them together. In this case, we have a pair of 2s, which we can simplify to 2 * 2 = 4.

Step 3: Write the remaining prime factors under the square root symbol. In this case, we have 3 * 5 = 15.

Step 4: Combine the simplified pair of prime factors with the remaining prime factors under the square root symbol. We have √(4 * 15).

Step 5: Simplify the expression under the square root symbol by multiplying the simplified pair of prime factors with the remaining prime factors. We have √60.

Step 6: Factorize the number under the square root symbol into its prime factors. We can divide 60 by 2 to get 30, and then divide 30 by 2 to get 15. The prime factors of 60 are 2, 2, 3, and 5.

Step 7: Take out any pairs of the same prime factors and multiply them together. In this case, we have a pair of 2s, which we can simplify to 2 * 2 = 4.

Step 8: Write the remaining prime factors under the square root symbol. In this case, we have 3 * 5 = 15.

Step 9: Combine the simplified pair of prime factors with the remaining prime factors under the square root symbol. We have √(4 * 15).

Step 10: Simplify the expression under the square root symbol by multiplying the simplified pair of prime factors with the remaining prime factors. We have √60.

Step 11: Simplify the expression further by taking out the simplified pair of prime factors outside the square root symbol. We have 2√15.

Conclusion

In conclusion, simplifying the square root of 30 requires factorizing the number into its prime factors and simplifying any pairs of the same prime factors. By following the above step-by-step guide, we can simplify the square root of 30 to 2√15. Teachers can use this guide to help students understand the process of simplifying square roots and apply it to similar problems.