Which Of The Following Is Equal To $10$?A. $\sqrt{100}$ B. $\sqrt{81}$ C. $\sqrt{144}$ D. $\sqrt{121}$

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Introduction

In mathematics, square roots are a fundamental concept that deals with the number that, when multiplied by itself, gives a specified value. In this article, we will explore which of the given options is equal to 10. We will analyze each option and determine its square root value to find the correct answer.

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 is denoted by the symbol √.

Analyzing the Options

Let's analyze each option given in the problem:

Option A: 100\sqrt{100}

The square root of 100 is a value that, when multiplied by itself, gives 100. We know that 10 multiplied by 10 equals 100. Therefore, the square root of 100 is 10.

Option B: 81\sqrt{81}

The square root of 81 is a value that, when multiplied by itself, gives 81. We know that 9 multiplied by 9 equals 81. Therefore, the square root of 81 is 9.

Option C: 144\sqrt{144}

The square root of 144 is a value that, when multiplied by itself, gives 144. We know that 12 multiplied by 12 equals 144. Therefore, the square root of 144 is 12.

Option D: 121\sqrt{121}

The square root of 121 is a value that, when multiplied by itself, gives 121. We know that 11 multiplied by 11 equals 121. Therefore, the square root of 121 is 11.

Conclusion

In conclusion, the square root of 100 is 10. Therefore, the correct answer is option A: 100\sqrt{100}.

Why is Understanding Square Roots Important?

Understanding square roots is crucial in mathematics and real-life applications. Square roots are used in various mathematical operations, such as solving equations and finding the area and perimeter of shapes. In real-life applications, square roots are used in finance, engineering, and physics to calculate interest rates, distances, and velocities.

Real-Life Applications of Square Roots

Square roots have numerous real-life applications. Some of the most common applications include:

  • Finance: Square roots are used to calculate interest rates and investment returns.
  • Engineering: Square roots are used to calculate distances, velocities, and accelerations in engineering applications.
  • Physics: Square roots are used to calculate energies, forces, and velocities in physics applications.
  • Geometry: Square roots are used to calculate the area and perimeter of shapes.

Tips for Solving Square Root Problems

To solve square root problems, follow these tips:

  • Understand the concept of square roots: Make sure you understand what a square root is and how it is calculated.
  • Identify the square root value: Identify the square root value that is being asked for in the problem.
  • Calculate the square root: Calculate the square root value using the given information.
  • Check your answer: Check your answer to ensure it is correct.

Common Mistakes to Avoid

When solving square root problems, avoid the following common mistakes:

  • Not understanding the concept of square roots: Make sure you understand what a square root is and how it is calculated.
  • Not identifying the square root value: Identify the square root value that is being asked for in the problem.
  • Not calculating the square root: Calculate the square root value using the given information.
  • Not checking your answer: Check your answer to ensure it is correct.

Conclusion

Introduction

In our previous article, we discussed the concept of square roots and how to solve square root problems. In this article, we will answer some frequently asked questions (FAQs) 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 calculate the square root of a number?

A: To calculate the square root of a number, you can use a calculator or a mathematical formula. The formula for calculating the square root of a number is:

√x = y, where x is the number and y is the square root of x.

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

A: A square root and a square are related but different concepts. A square is a number that is multiplied by itself, while a square root is the value that, when multiplied by itself, gives the original number.

Q: Can I have a negative square root?

A: Yes, you can have a negative square root. For example, the square root of -16 is -4 because -4 multiplied by -4 equals -16.

Q: How do I simplify a square root expression?

A: To simplify a square root expression, you can use the following steps:

  1. Factor the number inside the square root sign.
  2. Look for any perfect squares that can be factored out.
  3. Simplify the expression by canceling out any common factors.

Q: What is the square root of a fraction?

A: The square root of a fraction is the square root of the numerator divided by the square root of the denominator. For example, the square root of 1/4 is 1/2 because the square root of 1 is 1 and the square root of 4 is 2.

Q: Can I have a square root of a decimal number?

A: Yes, you can have a square root of a decimal number. For example, the square root of 0.16 is 0.4 because 0.4 multiplied by 0.4 equals 0.16.

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

A: To calculate the square root of a negative number, you can use the following formula:

√(-x) = i√x, where i is the imaginary unit and x is the number.

Q: What is the square root of 0?

A: The square root of 0 is 0 because 0 multiplied by 0 equals 0.

Conclusion

In conclusion, understanding square roots is crucial in mathematics and real-life applications. By answering these frequently asked questions, we hope to provide a better understanding of square roots and how to solve square root problems.

Common Misconceptions About Square Roots

Here are some common misconceptions about square roots:

  • Square roots are only used in mathematics: Square roots are used in various real-life applications, such as finance, engineering, and physics.
  • Square roots are only used with positive numbers: Square roots can be used with negative numbers, and the result will be an imaginary number.
  • Square roots are only used with integers: Square roots can be used with decimals and fractions, and the result will be a decimal or fraction.

Conclusion

In conclusion, understanding square roots is crucial in mathematics and real-life applications. By understanding the concept of square roots and how to solve square root problems, you can apply this knowledge to various fields and make informed decisions.