Evaluate $\sqrt[3]{(x-y)(x+y)}$ When $x=76$ And $y=49$.

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Introduction

In this article, we will evaluate the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$. This involves substituting the given values of $x$ and $y$ into the expression and simplifying it to obtain the final result.

Understanding the Expression

The given expression is $\sqrt[3]{(x-y)(x+y)}$. This expression involves the difference of squares, which can be simplified using the formula $(a-b)(a+b) = a^2 - b^2$. In this case, we have $(x-y)(x+y) = x^2 - y^2$.

Substituting the Values of $x$ and $y$

We are given that $x=76$ and $y=49$. We can substitute these values into the expression $x^2 - y^2$ to obtain:

$$76^2 - 49^2$$

Evaluating the Expression

To evaluate the expression $76^2 - 49^2$, we can use the formula for the difference of squares:

$$(a^2 - b^2) = (a+b)(a-b)$$

In this case, we have:

$$(76^2 - 49^2) = (76+49)(76-49)$$

Simplifying the Expression

We can simplify the expression $(76+49)(76-49)$ by evaluating the products:

$$(76+49) = 125$$

$$(76-49) = 27$$

Evaluating the Final Expression

Now that we have simplified the expression, we can evaluate the final expression:

$$\sqrt[3]{(x-y)(x+y)} = \sqrt[3]{(125)(27)}$$

Evaluating the Cube Root

To evaluate the cube root of $(125)(27)$, we can use the property of cube roots that states:

$$\sqrt[3]{a^3} = a$$

In this case, we have:

$$\sqrt[3]{(125)(27)} = \sqrt[3]{(5^3)(3^3)}$$

Simplifying the Cube Root

We can simplify the cube root of $(5^3)(3^3)$ by using the property of cube roots:

$$\sqrt[3]{(5^3)(3^3)} = 5 \cdot 3$$

Evaluating the Final Result

Now that we have simplified the cube root, we can evaluate the final result:

$$\sqrt[3]{(x-y)(x+y)} = 5 \cdot 3 = 15$$

Conclusion

In this article, we evaluated the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$. We substituted the given values of $x$ and $y$ into the expression, simplified it using the formula for the difference of squares, and evaluated the final result to obtain the final answer of $15$.

Frequently Asked Questions

• What is the value of $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$?
• How do you simplify the expression $\sqrt[3]{(x-y)(x+y)}$?
• What is the final result of evaluating the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$?

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Further Reading

• [1] "Introduction to Algebra" by Richard Rusczyk
• [2] "Calculus for Dummies" by Mark Ryan
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Related Topics

• [1] "Evaluating Expressions with Exponents"
• [2] "Simplifying Expressions with Fractions"
• [3] "Evaluating Expressions with Variables"
  

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Introduction

In our previous article, we evaluated the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the value of $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$?

A: The value of $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$ is $15$.

Q: How do you simplify the expression $\sqrt[3]{(x-y)(x+y)}$?

A: To simplify the expression $\sqrt[3]{(x-y)(x+y)}$, we can use the formula for the difference of squares: $(a-b)(a+b) = a^2 - b^2$. We can then substitute the values of $x$ and $y$ into the expression and simplify it.

Q: What is the final result of evaluating the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$?

A: The final result of evaluating the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$ is $15$.

Q: Can you explain the steps involved in evaluating the expression $\sqrt[3]{(x-y)(x+y)}$?

A: Yes, the steps involved in evaluating the expression $\sqrt[3]{(x-y)(x+y)}$ are as follows:

1. Substitute the values of $x$ and $y$ into the expression.
2. Simplify the expression using the formula for the difference of squares.
3. Evaluate the cube root of the simplified expression.

Q: What is the significance of the cube root in this expression?

A: The cube root is used to evaluate the expression $\sqrt[3]{(x-y)(x+y)}$ because it allows us to find the value of the expression when $x=76$ and $y=49$.

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

A: Yes, here are a few more examples:

• Evaluate $\sqrt[3]{(2x-3)(2x+3)}$ when $x=4$.
• Evaluate $\sqrt[3]{(x+2)(x-2)}$ when $x=5$.
• Evaluate $\sqrt[3]{(3x-2)(3x+2)}$ when $x=3$.

Conclusion

In this article, we answered some frequently asked questions related to evaluating the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$. We provided step-by-step instructions on how to simplify the expression and evaluate the final result.

Frequently Asked Questions

• What is the value of $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$?
• How do you simplify the expression $\sqrt[3]{(x-y)(x+y)}$?
• What is the final result of evaluating the expression $\sqrt[3]{(x-y)(x+y)}$ when $x=76$ and $y=49$?
• Can you explain the steps involved in evaluating the expression $\sqrt[3]{(x-y)(x+y)}$?
• What is the significance of the cube root in this expression?
• Can you provide more examples of evaluating expressions with cube roots?

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Further Reading

• [1] "Introduction to Algebra" by Richard Rusczyk
• [2] "Calculus for Dummies" by Mark Ryan
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Related Topics

• [1] "Evaluating Expressions with Exponents"
• [2] "Simplifying Expressions with Fractions"
• [3] "Evaluating Expressions with Variables"