Which Of The Following Are Square Roots Of The Number Below? Check All That Apply.Number: 100A. 10 B. 50 C. -10 D. 5 E. $100^{1 / 2}$ F. $-100^{1 / 2}$

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Which of the Following are Square Roots of the Number Below? Check All That Apply

Understanding Square Roots

In mathematics, 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 Number in Question: 100

We are given the number 100 and asked to determine which of the following options are its square roots. Let's examine each option carefully.

Option A: 10

To determine if 10 is a square root of 100, we need to check if 10 multiplied by 10 equals 100. Indeed, 10 multiplied by 10 equals 100, so 10 is a square root of 100.

Option B: 50

To determine if 50 is a square root of 100, we need to check if 50 multiplied by 50 equals 100. However, 50 multiplied by 50 equals 2500, not 100. Therefore, 50 is not a square root of 100.

Option C: -10

To determine if -10 is a square root of 100, we need to check if -10 multiplied by -10 equals 100. Indeed, -10 multiplied by -10 equals 100, so -10 is a square root of 100.

Option D: 5

To determine if 5 is a square root of 100, we need to check if 5 multiplied by 5 equals 100. However, 5 multiplied by 5 equals 25, not 100. Therefore, 5 is not a square root of 100.

Option E: $100^{1 / 2}$

This option represents the square root of 100 using exponent notation. To evaluate this expression, we need to apply the rule of exponents that states $a^{m/n} = \sqrt[n]{a^m}$. In this case, $100^{1 / 2} = \sqrt{100} = 10$. Therefore, $100^{1 / 2}$ is a square root of 100.

Option F: $-100^{1 / 2}$

This option represents the negative square root of 100 using exponent notation. To evaluate this expression, we need to apply the rule of exponents that states $a^{m/n} = \sqrt[n]{a^m}$. In this case, $-100^{1 / 2} = -\sqrt{100} = -10$. Therefore, $-100^{1 / 2}$ is a square root of 100.

Conclusion

In conclusion, the square roots of the number 100 are 10, -10, $100^{1 / 2}$, and $-100^{1 / 2}$. These values satisfy the definition of a square root, as they, when multiplied by themselves, give the original number 100.

Key Takeaways

  • A square root of a number is a value that, when multiplied by itself, gives the original number.
  • The square root of a number can be either positive or negative.
  • To determine if a value is a square root of a number, we need to check if the value multiplied by itself equals the original number.
  • The square roots of the number 100 are 10, -10, $100^{1 / 2}$, and $-100^{1 / 2}$.

Further Exploration

  • What are the square roots of the number 25?
  • What are the square roots of the number 36?
  • How do we find the square root of a negative number?
  • What is the relationship between square roots and exponents?

References

Additional Resources

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

A: To find the square root of a number, you can use a calculator or a mathematical formula. The formula for finding the square root of a number is: √x = y, where x is the number and y is the square root.

Q: What are the square roots of the number 100?

A: The square roots of the number 100 are 10 and -10. These values satisfy the definition of a square root, as they, when multiplied by themselves, give the original number 100.

Q: Can a square root be a negative number?

A: Yes, a square root can be a negative number. For example, the square root of 16 is 4, but the square root of -16 is -4.

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

A: To find the square root of a negative number, you can use the formula: √(-x) = i√x, where i is the imaginary unit and x is the number.

Q: What is the relationship between square roots and exponents?

A: The square root of a number is equivalent to raising the number to the power of 1/2. For example, the square root of 16 is 4, which is equivalent to 16^(1/2).

Q: Can I use a calculator to find the square root of a number?

A: Yes, you can use a calculator to find the square root of a number. Most calculators have a √ button that you can press to find the square root of a number.

Q: How do I simplify a square root expression?

A: To simplify a square root expression, you can look for perfect squares that can be factored out of the expression. For example, the square root of 16 can be simplified as √16 = √(4^2) = 4.

Q: What are some common mistakes to avoid when working with square roots?

A: Some common mistakes to avoid when working with square roots include:

  • Not considering the negative square root of a number
  • Not simplifying square root expressions
  • Not using the correct formula for finding the square root of a negative number

Q: How do I use square roots in real-world applications?

A: Square roots are used in a variety of real-world applications, including:

  • Calculating distances and heights
  • Finding the area and perimeter of shapes
  • Solving problems in physics and engineering
  • Working with financial data and statistics

Q: What are some advanced topics related to square roots?

A: Some advanced topics related to square roots include:

  • Imaginary numbers and complex numbers
  • Quadratic equations and formulas
  • Higher-order roots and radicals
  • Advanced mathematical techniques and formulas

References

Additional Resources