Evaluate The Expression: 360 = \sqrt{360}= 360 =

Mar 11, 2025 by ADMIN 51 views

$Evaluate the Expression: $\sqrt{360}$$

Introduction

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. The square root is denoted by the symbol $\sqrt{}$ . In this article, we will evaluate the expression $\sqrt{360}$ and find its value.

Understanding the Square Root

The square root of a number can be a rational or irrational number. A rational number is a number that can be expressed as the ratio of two integers, while an irrational number is a number that cannot be expressed as a ratio of two integers. The square root of a number can be found using various methods, including the prime factorization method, the long division method, and the calculator method.

Prime Factorization Method

One of the methods to find the square root of a number is the prime factorization method. This method involves breaking down the number into its prime factors and then finding the square root of each factor. The prime factorization of 360 is $2^3 \times 3^2 \times 5$ . To find the square root of 360, we need to find the square root of each prime factor and then multiply them together.

Finding the Square Root of Prime Factors

To find the square root of each prime factor, we need to find the square root of 2, 3, and 5. The square root of 2 is approximately 1.414, the square root of 3 is approximately 1.732, and the square root of 5 is approximately 2.236.

Multiplying the Square Roots

Now that we have found the square root of each prime factor, we can multiply them together to find the square root of 360. The square root of 360 is approximately $2^1.5 \times 3^1 \times 5^0.5$ .

Simplifying the Expression

To simplify the expression, we can combine the exponents of the prime factors. The expression $2^1.5 \times 3^1 \times 5^0.5$ can be simplified to $2^1 \times 2^0.5 \times 3^1 \times 5^0.5$ .

Evaluating the Expression

Now that we have simplified the expression, we can evaluate it to find the value of $\sqrt{360}$ . The value of $\sqrt{360}$ is approximately $2 \times 1.414 \times 3 \times 2.236$ .

Calculating the Value

To calculate the value of $\sqrt{360}$ , we need to multiply the numbers together. The value of $\sqrt{360}$ is approximately $2 \times 1.414 \times 3 \times 2.236 = 18.00$ .

Conclusion

In this article, we evaluated the expression $\sqrt{360}$ and found its value. We used the prime factorization method to break down the number into its prime factors and then found the square root of each factor. We multiplied the square roots together to find the square root of 360 and then simplified the expression to find the value of $\sqrt{360}$ . The value of $\sqrt{360}$ is approximately 18.00.

Final Answer

The final answer to the expression $\sqrt{360}$ is $\boxed{18.00}$ .

References

[1] "Square Root" by Math Open Reference
[2] "Prime Factorization" by Math Is Fun
[3] "Long Division" by Khan Academy
[4] "Calculator Method" by Wolfram Alpha

Introduction

In our previous article, we evaluated the expression $\sqrt{360}$ and found its value to be approximately 18.00. In this article, we will answer some frequently asked questions related to the expression $\sqrt{360}$ .

Q1: What is the square root of 360?

A1: The square root of 360 is approximately 18.00.

Q2: How do you find the square root of 360?

A2: To find the square root of 360, you can use the prime factorization method, which involves breaking down the number into its prime factors and then finding the square root of each factor.

Q3: What is the prime factorization of 360?

A3: The prime factorization of 360 is $2^3 \times 3^2 \times 5$ .

Q4: How do you find the square root of each prime factor?

A4: To find the square root of each prime factor, you need to find the square root of 2, 3, and 5. The square root of 2 is approximately 1.414, the square root of 3 is approximately 1.732, and the square root of 5 is approximately 2.236.

Q5: How do you multiply the square roots together?

A5: To multiply the square roots together, you need to multiply the square roots of each prime factor. The square root of 360 is approximately $2^1.5 \times 3^1 \times 5^0.5$ .

Q6: How do you simplify the expression?

A6: To simplify the expression, you can combine the exponents of the prime factors. The expression $2^1.5 \times 3^1 \times 5^0.5$ can be simplified to $2^1 \times 2^0.5 \times 3^1 \times 5^0.5$ .

Q7: What is the final value of $\sqrt{360}$ ?

A7: The final value of $\sqrt{360}$ is approximately 18.00.

Q8: Can you use a calculator to find the square root of 360?

A8: Yes, you can use a calculator to find the square root of 360. The calculator method is a quick and easy way to find the square root of a number.

Q9: What are some related topics to the expression $\sqrt{360}$ ?

A9: Some related topics to the expression $\sqrt{360}$ include square root of a number, prime factorization method, long division method, and calculator method.

Q10: Where can I find more information about the expression $\sqrt{360}$ ?

A10: You can find more information about the expression $\sqrt{360}$ on websites such as Math Open Reference, Math Is Fun, and Wolfram Alpha.

Conclusion

In this article, we answered some frequently asked questions related to the expression $\sqrt{360}$ . We provided step-by-step instructions on how to find the square root of 360 and simplified the expression to find the final value. We also provided related topics and resources for further learning.

Final Answer

The final answer to the expression $\sqrt{360}$ is $\boxed{18.00}$ .

References

[1] "Square Root" by Math Open Reference
[2] "Prime Factorization" by Math Is Fun
[3] "Long Division" by Khan Academy
[4] "Calculator Method" by Wolfram Alpha

Evaluate The Expression: 360 = \sqrt{360}= 360 =

Introduction

Understanding the Square Root

Prime Factorization Method

Finding the Square Root of Prime Factors

Multiplying the Square Roots

Simplifying the Expression

Evaluating the Expression

Calculating the Value

Conclusion

Final Answer

Related Topics

References

Further Reading

Introduction

Q1: What is the square root of 360?

Q2: How do you find the square root of 360?

Q3: What is the prime factorization of 360?

Q4: How do you find the square root of each prime factor?

Q5: How do you multiply the square roots together?

Q6: How do you simplify the expression?

Q7: What is the final value of $\sqrt{360}$ ?

Q8: Can you use a calculator to find the square root of 360?

Q9: What are some related topics to the expression $\sqrt{360}$ ?

Q10: Where can I find more information about the expression $\sqrt{360}$ ?

Conclusion

Final Answer

Related Topics

References

Further Reading

Introduction

Understanding the Square Root

Prime Factorization Method

Finding the Square Root of Prime Factors

Multiplying the Square Roots

Simplifying the Expression

Evaluating the Expression

Calculating the Value

Conclusion

Final Answer

Related Topics

References

Further Reading

Introduction

Q1: What is the square root of 360?

Q2: How do you find the square root of 360?

Q3: What is the prime factorization of 360?

Q4: How do you find the square root of each prime factor?

Q5: How do you multiply the square roots together?

Q6: How do you simplify the expression?

Q7: What is the final value of 360\sqrt{360}360​?

Q8: Can you use a calculator to find the square root of 360?

Q9: What are some related topics to the expression 360\sqrt{360}360​?

Q10: Where can I find more information about the expression 360\sqrt{360}360​?

Conclusion

Final Answer

Related Topics

References

Further Reading

Q7: What is the final value of $\sqrt{360}$ ?

Q9: What are some related topics to the expression $\sqrt{360}$ ?

Q10: Where can I find more information about the expression $\sqrt{360}$ ?