Evaluate The Expression: $\[ \sqrt{1.25} \\]

by ADMIN 45 views

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by applying the order of operations. In this article, we will focus on evaluating the expression 1.25\sqrt{1.25}, which involves finding the square root of a decimal number. We will explore the steps involved in evaluating this expression and provide a detailed explanation of the process.

Understanding Square Roots

Before we dive into evaluating the expression 1.25\sqrt{1.25}, it's essential to understand what square roots are. 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. In mathematical notation, this is represented as 16=4\sqrt{16} = 4.

Evaluating the Expression

To evaluate the expression 1.25\sqrt{1.25}, we need to find the value that, when multiplied by itself, gives 1.25. This involves finding the square root of 1.25.

Step 1: Simplify the Expression

The first step in evaluating the expression 1.25\sqrt{1.25} is to simplify it. We can simplify the expression by breaking it down into its prime factors. In this case, 1.25 can be expressed as 1.25=1.25Γ—1=1.25Γ—54=54Γ—54=25161.25 = 1.25 \times 1 = 1.25 \times \frac{5}{4} = \frac{5}{4} \times \frac{5}{4} = \frac{25}{16}.

Step 2: Find the Square Root

Now that we have simplified the expression, we can find the square root of 2516\frac{25}{16}. To do this, we need to find the square root of the numerator and the denominator separately. The square root of 25 is 5, and the square root of 16 is 4.

Step 3: Simplify the Result

Now that we have found the square root of the numerator and the denominator, we can simplify the result. The square root of 2516\frac{25}{16} is 2516=54\frac{\sqrt{25}}{\sqrt{16}} = \frac{5}{4}.

Conclusion

In conclusion, evaluating the expression 1.25\sqrt{1.25} involves finding the square root of a decimal number. We simplified the expression by breaking it down into its prime factors, found the square root of the numerator and the denominator separately, and simplified the result. The final answer is 54\frac{5}{4}.

Frequently Asked Questions

  • What is the square root of 1.25?
  • How do you evaluate the expression 1.25\sqrt{1.25}?
  • What is the simplified form of the expression 1.25\sqrt{1.25}?

Final Answer

The final answer is 54\boxed{\frac{5}{4}}.

Additional Resources

Related Articles

References

Introduction

Evaluating expressions with square roots can be a challenging task, especially when dealing with decimal numbers. In our previous article, we explored the process of evaluating the expression 1.25\sqrt{1.25} and provided a step-by-step guide on how to simplify it. In this article, we will answer some of the most frequently asked questions related to evaluating expressions with square roots.

Q&A

Q: What is the square root of 1.25?

A: The square root of 1.25 is 54\frac{5}{4}.

Q: How do you evaluate the expression 1.25\sqrt{1.25}?

A: To evaluate the expression 1.25\sqrt{1.25}, you need to simplify it by breaking it down into its prime factors. Then, find the square root of the numerator and the denominator separately, and simplify the result.

Q: What is the simplified form of the expression 1.25\sqrt{1.25}?

A: The simplified form of the expression 1.25\sqrt{1.25} is 54\frac{5}{4}.

Q: Can you provide more examples of evaluating expressions with square roots?

A: Yes, here are a few more examples:

  • 4=2\sqrt{4} = 2
  • 9=3\sqrt{9} = 3
  • 16=4\sqrt{16} = 4
  • 25=5\sqrt{25} = 5

Q: How do you handle negative numbers when evaluating expressions with square roots?

A: When evaluating expressions with square roots, you need to consider the sign of the number inside the square root. If the number is negative, the square root will be an imaginary number.

Q: Can you provide more information on imaginary numbers?

A: Yes, imaginary numbers are a type of complex number that can be represented as a+bia + bi, where aa and bb are real numbers and ii is the imaginary unit. Imaginary numbers are used to extend the real number system to include numbers that cannot be expressed as a ratio of integers.

Q: How do you handle decimal numbers when evaluating expressions with square roots?

A: When evaluating expressions with square roots, you need to simplify the decimal number by breaking it down into its prime factors. Then, find the square root of the numerator and the denominator separately, and simplify the result.

Q: Can you provide more information on simplifying decimal numbers?

A: Yes, simplifying decimal numbers involves breaking them down into their prime factors. For example, the decimal number 1.25 can be expressed as 54\frac{5}{4}.

Conclusion

Evaluating expressions with square roots can be a challenging task, but with the right tools and techniques, it can be done easily. In this article, we answered some of the most frequently asked questions related to evaluating expressions with square roots and provided a step-by-step guide on how to simplify them.

Frequently Asked Questions

  • What is the square root of 1.25?
  • How do you evaluate the expression 1.25\sqrt{1.25}?
  • What is the simplified form of the expression 1.25\sqrt{1.25}?
  • Can you provide more examples of evaluating expressions with square roots?
  • How do you handle negative numbers when evaluating expressions with square roots?
  • Can you provide more information on imaginary numbers?
  • How do you handle decimal numbers when evaluating expressions with square roots?
  • Can you provide more information on simplifying decimal numbers?

Final Answer

The final answer is 54\boxed{\frac{5}{4}}.

Additional Resources

Related Articles

References