Evaluate The Expression: $\sqrt{25}$.Choose The Set(s) Of Numbers To Which The Result Belongs:A. NaturalB. WholeC. IntegersD. RationalsE. IrrationalsF. Real

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Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical expressions by applying the rules of arithmetic operations. In this article, we will evaluate the expression $\sqrt{25}$ and determine the set(s) of numbers to which the result belongs.

What is the Square Root of 25?

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, if $x$ is the square root of $y$, then $x^2 = y$. The square root of 25 is a value that, when multiplied by itself, gives 25.

Calculating the Square Root of 25

To calculate the square root of 25, we can use the fact that $5^2 = 25$. Therefore, the square root of 25 is 5.

Evaluating the Expression: $\sqrt{25} = 5$

Now that we have calculated the square root of 25, we can evaluate the expression $\sqrt{25}$. The result is 5.

Which Set(s) of Numbers Does the Result Belong To?

The result, 5, belongs to several sets of numbers. Let's evaluate each option:

A. Natural Numbers

Natural numbers are positive integers, starting from 1. The result, 5, is a positive integer, so it belongs to the set of natural numbers.

B. Whole Numbers

Whole numbers are non-negative integers, starting from 0. The result, 5, is a non-negative integer, so it belongs to the set of whole numbers.

C. Integers

Integers are whole numbers, including negative numbers. The result, 5, is a whole number, but it is not negative, so it belongs to the set of integers.

D. Rationals

Rational numbers are numbers that can be expressed as the ratio of two integers. The result, 5, can be expressed as the ratio of 5/1, so it belongs to the set of rational numbers.

E. Irrationals

Irrational numbers are numbers that cannot be expressed as the ratio of two integers. The result, 5, can be expressed as the ratio of 5/1, so it does not belong to the set of irrational numbers.

F. Real Numbers

Real numbers are all numbers, including rational and irrational numbers. The result, 5, is a rational number, so it belongs to the set of real numbers.

Conclusion

In conclusion, the result of the expression $\sqrt{25}$ is 5, which belongs to the sets of natural numbers, whole numbers, integers, rationals, and real numbers.

Key Takeaways

• The square root of 25 is 5.
• The result, 5, belongs to the sets of natural numbers, whole numbers, integers, rationals, and real numbers.
• The result, 5, does not belong to the set of irrational numbers.

Final Thoughts

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Introduction

In our previous article, we evaluated the expression $\sqrt{25}$ and determined the set(s) of numbers to which the result belongs. In this article, we will answer some frequently asked questions related to the expression $\sqrt{25}$.

Q&A

Q: What is the square root of 25?

A: The square root of 25 is a value that, when multiplied by itself, gives 25. In other words, if $x$ is the square root of 25, then $x^2 = 25$. The square root of 25 is 5.

Q: Why is the square root of 25 equal to 5?

A: The square root of 25 is equal to 5 because $5^2 = 25$. This means that 5 multiplied by itself gives 25.

Q: Which set(s) of numbers does the result belong to?

A: The result, 5, belongs to the sets of natural numbers, whole numbers, integers, rationals, and real numbers.

Q: Why does the result not belong to the set of irrational numbers?

A: The result, 5, can be expressed as the ratio of 5/1, so it belongs to the set of rational numbers. Irrational numbers are numbers that cannot be expressed as the ratio of two integers.

Q: Can the result be expressed as a decimal?

A: Yes, the result, 5, can be expressed as a decimal. In fact, 5 is equal to 5.0.

Q: Is the result a perfect square?

A: Yes, the result, 5, is a perfect square because it can be expressed as the square of an integer (5^2 = 25).

Q: Can the result be expressed as a fraction?

A: Yes, the result, 5, can be expressed as a fraction. In fact, 5 is equal to 5/1.

Q: Is the result a whole number?

A: Yes, the result, 5, is a whole number because it is a non-negative integer.

Q: Is the result a positive integer?

A: Yes, the result, 5, is a positive integer because it is a positive whole number.

Q: Can the result be expressed as a negative number?

A: No, the result, 5, cannot be expressed as a negative number because it is a positive integer.

Q: Is the result an integer?

A: Yes, the result, 5, is an integer because it is a whole number.

Q: Is the result a rational number?

A: Yes, the result, 5, is a rational number because it can be expressed as the ratio of two integers (5/1).

Q: Is the result a real number?

A: Yes, the result, 5, is a real number because it is a rational number.

Conclusion

In conclusion, we have answered some frequently asked questions related to the expression $\sqrt{25}$. We hope that this article has provided you with a better understanding of the expression and its properties.

Key Takeaways

• The square root of 25 is 5.
• The result, 5, belongs to the sets of natural numbers, whole numbers, integers, rationals, and real numbers.
• The result, 5, does not belong to the set of irrational numbers.
• The result, 5, can be expressed as a decimal, a fraction, and a whole number.
• The result, 5, is a perfect square and a positive integer.

Final Thoughts

Evaluating mathematical expressions is an essential skill in mathematics. By understanding the rules of arithmetic operations and the properties of numbers, we can simplify complex expressions and determine the set(s) of numbers to which the result belongs. In this article, we have answered some frequently asked questions related to the expression $\sqrt{25}$ and provided you with a better understanding of the expression and its properties.