Simplify: 144 \sqrt{144} 144 A. 12 And -12 B. 12 C. -12 D. 72 E. -72

Mar 9, 2025 by ADMIN 75 views

Simplifying Square Roots: A Step-by-Step Guide

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Introduction

Simplifying square roots is an essential skill in mathematics, particularly in algebra and geometry. It involves finding the simplest form of a square root expression, which can be a single number or a product of numbers. In this article, we will explore the concept of simplifying square roots, focusing on the square root of 144.

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 multiplied by 4 equals 16. The square root of a number can be positive or negative.

Simplifying Square Roots

To simplify a square root, we need to find the largest perfect square that divides the number inside the square root. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4.

Simplifying the Square Root of 144

Now, let's simplify the square root of 144. To do this, we need to find the largest perfect square that divides 144.

Step 1: Find the Factors of 144

The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

Step 2: Identify the Perfect Squares

The perfect squares among the factors of 144 are: 1, 4, 9, 16, 36, and 144.

Step 3: Simplify the Square Root

Now, let's simplify the square root of 144 by finding the largest perfect square that divides 144. We can see that 144 is equal to 12 multiplied by 12, which is a perfect square.

Conclusion

In conclusion, the square root of 144 can be simplified to 12, because 12 multiplied by 12 equals 144. Therefore, the correct answer is:

The Final Answer is: 12

Frequently Asked Questions

Q: What is the square root of 144?

A: The square root of 144 is 12.

Q: Can the square root of 144 be negative?

A: Yes, the square root of 144 can be negative, but in this case, we are only considering the positive square root.

Q: How do I simplify a square root?

A: To simplify a square root, you need to find the largest perfect square that divides the number inside the square root.

Additional Resources

For more information on simplifying square roots, you can check out the following resources:

Khan Academy: Simplifying Square Roots
Mathway: Simplifying Square Roots
Wolfram Alpha: Simplifying Square Roots

Final Thoughts

Simplifying square roots is an essential skill in mathematics, and it can be applied to a wide range of problems. By following the steps outlined in this article, you can simplify square roots with ease. Remember to always look for the largest perfect square that divides the number inside the square root, and you will be able to simplify square roots like a pro!

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Introduction

In our previous article, we explored the concept of simplifying square roots, focusing on the square root of 144. We discussed the importance of finding the largest perfect square that divides the number inside the square root. In this article, we will continue to delve deeper into the world of simplifying square roots, answering some of the most frequently asked questions.

Q&A: Simplifying Square Roots

Q: What is the difference between a perfect square and a square root?

A: A perfect square is a number that can be expressed as the product of an integer with itself, while a square root is the value that, when multiplied by itself, gives the original number.

Q: How do I simplify a square root with a variable?

A: To simplify a square root with a variable, you need to find the largest perfect square that divides the expression inside the square root. For example, if you have √(x^2 + 4x + 4), you can simplify it to √((x + 2)^2).

Q: Can I simplify a square root with a negative number?

A: Yes, you can simplify a square root with a negative number. For example, if you have √(-16), you can simplify it to 4i, where i is the imaginary unit.

Q: How do I simplify a square root with a decimal number?

A: To simplify a square root with a decimal number, you need to find the largest perfect square that divides the decimal number. For example, if you have √(2.5), you can simplify it to 1.58113883, but it's often more useful to leave it in its radical form.

Q: Can I simplify a square root with a fraction?

A: Yes, you can simplify a square root with a fraction. For example, if you have √(1/4), you can simplify it to 1/2.

Q: How do I simplify a square root with a negative fraction?

A: To simplify a square root with a negative fraction, you need to find the largest perfect square that divides the fraction. For example, if you have √(-1/4), you can simplify it to -1/2.

Q: Can I simplify a square root with a complex number?

A: Yes, you can simplify a square root with a complex number. For example, if you have √(1 + 2i), you can simplify it to 1 + i.

Tips and Tricks

Tip 1: Always look for the largest perfect square that divides the number inside the square root.

This will help you simplify the square root and make it easier to work with.

Tip 2: Use the properties of square roots to simplify expressions.

For example, you can use the property √(ab) = √a√b to simplify expressions with multiple square roots.

Tip 3: Don't be afraid to use a calculator to check your work.

If you're unsure about the simplification of a square root, you can use a calculator to check your work and make sure you're getting the correct answer.