Evaluate The Expression:${ \sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25}) }$

Introduction

In this article, we will evaluate the given mathematical expression, which involves the use of cube roots and square roots. The expression is $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$. We will break down the expression into smaller parts, evaluate each part separately, and then combine the results to obtain the final answer.

Understanding the Cube Root

The cube root of a number is a value that, when multiplied by itself twice, gives the original number. In other words, if $x$ is the cube root of $y$, then $x^3 = y$. The cube root is denoted by the symbol $\sqrt[3]{y}$.

Evaluating the Inner Cube Root

The inner cube root in the given expression is $\sqrt[3]{27}$. To evaluate this, we need to find the cube root of 27. Since $3^3 = 27$, the cube root of 27 is 3.

Evaluating the Outer Cube Root

Now that we have evaluated the inner cube root, we can move on to the outer cube root. The outer cube root is $\sqrt[3]{\sqrt[3]{27}}$. Since we know that the inner cube root is 3, we can substitute this value into the outer cube root. Therefore, $\sqrt[3]{\sqrt[3]{27}} = \sqrt[3]{3}$. To evaluate this, we need to find the cube root of 3. Since $1.4422^3 \approx 3$, the cube root of 3 is approximately 1.4422.

Understanding the Square Root

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 is denoted by the symbol $\sqrt{y}$.

Evaluating the Negative Square Root

The given expression contains a negative square root, which is $-\sqrt{25}$. To evaluate this, we need to find the square root of 25. Since $5^2 = 25$, the square root of 25 is 5. However, since the square root is negative, the value is $-5$.

Combining the Results

Now that we have evaluated both the cube root and the square root, we can combine the results to obtain the final answer. The given expression is $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$. We have found that $\sqrt[3]{\sqrt[3]{27}} \approx 1.4422$ and $-\sqrt{25} = -5$. Therefore, the final answer is $1.4422 - (-5) = 1.4422 + 5 = 6.4422$.

Conclusion

In this article, we evaluated the given mathematical expression, which involved the use of cube roots and square roots. We broke down the expression into smaller parts, evaluated each part separately, and then combined the results to obtain the final answer. The final answer is $6.4422$.

Frequently Asked Questions

• What is the cube root of 27? The cube root of 27 is 3.
• What is the square root of 25? The square root of 25 is 5.
• What is the final answer to the given expression? The final answer is $6.4422$.

Final Answer

The final answer to the given expression is $\boxed{6.4422}$.

Introduction

In our previous article, we evaluated the mathematical expression $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$. We broke down the expression into smaller parts, evaluated each part separately, and then combined the results to obtain the final answer. In this article, we will answer some frequently asked questions related to the expression.

Q&A

Q1: What is the cube root of 27?

A1: The cube root of 27 is 3.

Q2: What is the square root of 25?

A2: The square root of 25 is 5.

Q3: How do you evaluate the expression $\sqrt[3]{\sqrt[3]{27}}$?

A3: To evaluate the expression $\sqrt[3]{\sqrt[3]{27}}$, we need to find the cube root of 27 first. Since $3^3 = 27$, the cube root of 27 is 3. Then, we take the cube root of 3, which is approximately 1.4422.

Q4: How do you evaluate the expression $-\sqrt{25}$?

A4: To evaluate the expression $-\sqrt{25}$, we need to find the square root of 25 first. Since $5^2 = 25$, the square root of 25 is 5. However, since the square root is negative, the value is $-5$.

Q5: What is the final answer to the given expression?

A5: The final answer to the given expression is $6.4422$.

Q6: Can you explain the concept of cube roots and square roots?

A6: Yes, certainly. The cube root of a number is a value that, when multiplied by itself twice, gives the original number. In other words, if $x$ is the cube root of $y$, then $x^3 = y$. The cube root is denoted by the symbol $\sqrt[3]{y}$. 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 is denoted by the symbol $\sqrt{y}$.

Q7: How do you simplify the expression $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$?

A7: To simplify the expression $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$, we need to evaluate the cube root and the square root separately. Then, we can combine the results to obtain the final answer.

Q8: What is the difference between the cube root and the square root?

A8: The cube root and the square root are both roots of a number, but they are different. The cube root is a value that, when multiplied by itself twice, gives the original number, while the square root is a value that, when multiplied by itself, gives the original number.

Conclusion

In this article, we answered some frequently asked questions related to the expression $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$. We explained the concept of cube roots and square roots, and we provided step-by-step solutions to the expression. We hope that this article has been helpful in understanding the concept of roots and how to simplify expressions involving roots.

Frequently Asked Questions

• What is the cube root of 27?
• What is the square root of 25?
• How do you evaluate the expression $\sqrt[3]{\sqrt[3]{27}}$?
• How do you evaluate the expression $-\sqrt{25}$?
• What is the final answer to the given expression?
• Can you explain the concept of cube roots and square roots?
• How do you simplify the expression $\sqrt[3]{\sqrt[3]{27}} - (-\sqrt{25})$?
• What is the difference between the cube root and the square root?

Final Answer

The final answer to the given expression is $\boxed{6.4422}$.