What Is The Simplified Value Of The Expression Below?$\frac{\sqrt{100}}{\sqrt{4}}$A. $\sqrt{98}$ B. $\sqrt{400}$ C. 5 D. 25

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What is the Simplified Value of the Expression Below?

The expression 1004\frac{\sqrt{100}}{\sqrt{4}} is a mathematical expression that involves the square root of two numbers. In this article, we will simplify this expression and find its value.

Understanding the Square Root

The 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 \sqrt{}. In the expression 1004\frac{\sqrt{100}}{\sqrt{4}}, we have two square roots: 100\sqrt{100} and 4\sqrt{4}.

Simplifying the Square Roots

To simplify the square roots, we need to find the values that, when multiplied by themselves, give the numbers inside the square roots. The square root of 100 is 10, because 10 multiplied by 10 equals 100. The square root of 4 is 2, because 2 multiplied by 2 equals 4.

Simplifying the Expression

Now that we have simplified the square roots, we can simplify the expression. We have 1004=102\frac{\sqrt{100}}{\sqrt{4}} = \frac{10}{2}. To simplify this expression, we can divide the numerator by the denominator. When we divide 10 by 2, we get 5.

Conclusion

In conclusion, the simplified value of the expression 1004\frac{\sqrt{100}}{\sqrt{4}} is 5. This is because the square roots of 100 and 4 are 10 and 2, respectively, and when we divide 10 by 2, we get 5.

Why is this Important?

Simplifying mathematical expressions is an important skill that is used in many areas of mathematics and science. It helps us to understand the underlying structure of mathematical expressions and to make calculations easier. In this article, we have seen how to simplify a mathematical expression involving square roots.

Real-World Applications

Simplifying mathematical expressions has many real-world applications. For example, in physics, we often need to simplify mathematical expressions to understand the behavior of physical systems. In engineering, we need to simplify mathematical expressions to design and build complex systems.

Common Mistakes

When simplifying mathematical expressions, there are several common mistakes that we can make. One common mistake is to forget to simplify the square roots. Another common mistake is to simplify the expression incorrectly. To avoid these mistakes, we need to be careful and methodical in our approach.

Tips and Tricks

Here are some tips and tricks for simplifying mathematical expressions:

  • Always simplify the square roots first.
  • Use the order of operations to simplify the expression.
  • Check your work carefully to avoid mistakes.
  • Use a calculator to check your work if necessary.

Conclusion

In conclusion, simplifying mathematical expressions is an important skill that is used in many areas of mathematics and science. By following the tips and tricks outlined in this article, we can simplify mathematical expressions and understand the underlying structure of mathematical expressions.

Final Answer

The final answer is: 5\boxed{5}
Frequently Asked Questions: Simplifying Mathematical Expressions

In this article, we will answer some frequently asked questions about simplifying mathematical expressions.

Q: What is the first step in simplifying a mathematical expression?

A: The first step in simplifying a mathematical expression is to simplify the square roots. This involves finding the values that, when multiplied by themselves, give the numbers inside the square roots.

Q: How do I simplify a square root?

A: To simplify a square root, you need to find the value that, when multiplied by itself, gives the number inside the square root. For example, the square root of 100 is 10, because 10 multiplied by 10 equals 100.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying a mathematical expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I use the order of operations to simplify a mathematical expression?

A: To use the order of operations to simplify a mathematical expression, follow these steps:

  1. Evaluate any expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a simplified expression and a simplified fraction?

A: A simplified expression is a mathematical expression that has been simplified by combining like terms and eliminating any unnecessary operations. A simplified fraction is a fraction that has been simplified by dividing both the numerator and the denominator by their greatest common divisor.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor. For example, the fraction 6/8 can be simplified by dividing both the numerator and the denominator by 2, resulting in the simplified fraction 3/4.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 6 and 8 is 2, because 2 is the largest number that divides both 6 and 8 without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the following steps:

  1. List the factors of each number.
  2. Identify the common factors.
  3. Choose the largest common factor.

Q: What is the difference between a simplified expression and a simplified equation?

A: A simplified expression is a mathematical expression that has been simplified by combining like terms and eliminating any unnecessary operations. A simplified equation is an equation that has been simplified by combining like terms and eliminating any unnecessary operations, and also by isolating the variable on one side of the equation.

Q: How do I simplify an equation?

A: To simplify an equation, you need to combine like terms and eliminate any unnecessary operations, and also isolate the variable on one side of the equation. For example, the equation 2x + 3 = 5 can be simplified by subtracting 3 from both sides, resulting in the simplified equation 2x = 2.

Q: What is the final answer to the expression 1004\frac{\sqrt{100}}{\sqrt{4}}?

A: The final answer to the expression 1004\frac{\sqrt{100}}{\sqrt{4}} is 5.

Conclusion

In conclusion, simplifying mathematical expressions is an important skill that is used in many areas of mathematics and science. By following the tips and tricks outlined in this article, we can simplify mathematical expressions and understand the underlying structure of mathematical expressions.

Final Answer

The final answer is: 5\boxed{5}