Which Of The Following Are Square Roots Of The Number Below? Check All That Apply.196A. 98 B. − 196 1 / 2 -196^{1/2} − 19 6 1/2 C. 14 D. 7 E. -14 F. 196 1 / 2 196^{1/2} 19 6 1/2

by ADMIN 182 views

Introduction

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. In this article, we will explore the square roots of the number 196 and determine which of the given options are correct.

Understanding Square Roots

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 either positive or negative, and both values are considered square roots of the number.

The Square Roots of 196

To find the square roots of 196, we need to find the values that, when multiplied by themselves, give 196. We can start by finding the positive square root of 196.

Finding the Positive Square Root of 196

To find the positive square root of 196, we can use the fact that the square root of a number is a value that, when multiplied by itself, gives the original number. We can start by finding the factors of 196.

Factors of 196

The factors of 196 are:

  • 1
  • 2
  • 4
  • 7
  • 14
  • 28
  • 49
  • 98
  • 196

We can see that 14 multiplied by 14 equals 196, so the positive square root of 196 is 14.

Finding the Negative Square Root of 196

Since the square root of a number can be either positive or negative, we also need to find the negative square root of 196.

The negative square root of 196 is -14, because -14 multiplied by -14 equals 196.

Evaluating the Options

Now that we have found the square roots of 196, we can evaluate the given options.

Option A: 98

Option A is 98. We can see that 98 is not a square root of 196, because 98 multiplied by 98 does not equal 196.

Option B: −1961/2-196^{1/2}

Option B is −1961/2-196^{1/2}. We can see that −1961/2-196^{1/2} is equal to -14, which is the negative square root of 196.

Option C: 14

Option C is 14. We can see that 14 is the positive square root of 196.

Option D: 7

Option D is 7. We can see that 7 is not a square root of 196, because 7 multiplied by 7 does not equal 196.

Option E: -14

Option E is -14. We can see that -14 is the negative square root of 196.

Option F: 1961/2196^{1/2}

Option F is 1961/2196^{1/2}. We can see that 1961/2196^{1/2} is equal to 14, which is the positive square root of 196.

Conclusion

In conclusion, the square roots of 196 are 14 and -14. Therefore, the correct options are:

  • Option B: −1961/2-196^{1/2}
  • Option C: 14
  • Option E: -14
  • Option F: 1961/2196^{1/2}

Introduction

In our previous article, we explored the square roots of the number 196 and determined which of the given options were correct. In this article, we will answer some frequently asked questions about square roots.

Q: What is a square root?

A: 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.

Q: Can a number have more than one square root?

A: Yes, a number can have more than one square root. For example, the square roots of 16 are 4 and -4, because 4 multiplied by 4 equals 16 and -4 multiplied by -4 equals 16.

Q: How do I find the square root of a number?

A: To find the square root of a number, you can use the fact that the square root of a number is a value that, when multiplied by itself, gives the original number. You can also use a calculator or a computer program to find the square root of a number.

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

A: The positive square root of a number is a value that, when multiplied by itself, gives the original number. The negative square root of a number is also a value that, when multiplied by itself, gives the original number, but it is the opposite of the positive square root.

Q: Can a number have a negative square root?

A: Yes, a number can have a negative square root. For example, the square roots of 16 are 4 and -4, because 4 multiplied by 4 equals 16 and -4 multiplied by -4 equals 16.

Q: How do I know if a number has a negative square root?

A: To determine if a number has a negative square root, you can try multiplying the number by itself and see if the result is positive or negative. If the result is negative, then the number has a negative square root.

Q: Can a number have a complex square root?

A: Yes, a number can have a complex square root. A complex square root is a square root that involves the imaginary unit i, which is defined as the square root of -1.

Q: How do I find the complex square root of a number?

A: To find the complex square root of a number, you can use the fact that the complex square root of a number is a value that, when multiplied by itself, gives the original number. You can also use a calculator or a computer program to find the complex square root of a number.

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

A: The real square root of a number is a value that, when multiplied by itself, gives the original number. The complex square root of a number is a value that, when multiplied by itself, gives the original number, but it involves the imaginary unit i.

Conclusion

In conclusion, square roots are an important concept in mathematics that can be used to solve a wide range of problems. By understanding the basics of square roots, you can use them to solve problems in algebra, geometry, and other areas of mathematics.

Common Mistakes to Avoid

When working with square roots, there are several common mistakes to avoid.

  • Not considering the negative square root: When finding the square root of a number, it's easy to forget to consider the negative square root. Make sure to consider both the positive and negative square roots of a number.
  • Not using the correct formula: When finding the square root of a number, make sure to use the correct formula. The formula for the square root of a number is x = ±√a, where x is the square root of a and a is the number.
  • Not checking for complex square roots: When finding the square root of a number, make sure to check for complex square roots. Complex square roots involve the imaginary unit i and can be used to solve problems in algebra and other areas of mathematics.

Tips and Tricks

When working with square roots, here are some tips and tricks to keep in mind.

  • Use a calculator or computer program: When finding the square root of a number, it's often easier to use a calculator or computer program. These tools can quickly and accurately find the square root of a number.
  • Check for negative square roots: When finding the square root of a number, make sure to check for negative square roots. Negative square roots can be used to solve problems in algebra and other areas of mathematics.
  • Use the correct formula: When finding the square root of a number, make sure to use the correct formula. The formula for the square root of a number is x = ±√a, where x is the square root of a and a is the number.