Simplify The Expression: { \sqrt{50} + \sqrt{20}$}$

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Introduction

In mathematics, simplifying expressions is an essential skill that helps us solve problems efficiently and accurately. When dealing with square roots, it's crucial to simplify the expression to make it easier to work with. In this article, we will simplify the expression $\sqrt{50} + \sqrt{20}$ using various mathematical techniques.

Understanding Square Roots

Before we dive into simplifying the expression, let's briefly review 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. We can represent square roots using the symbol $\sqrt{}$. For instance, $\sqrt{16}$ represents the square root of 16.

Simplifying $\sqrt{50}$

To simplify $\sqrt{50}$, we need to find the largest perfect square that divides 50. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it can be expressed as 4 multiplied by 4. In this case, the largest perfect square that divides 50 is 25, which is equal to 5 multiplied by 5.

We can rewrite $\sqrt{50}$ as $\sqrt{25 \times 2}$, because 50 can be expressed as 25 multiplied by 2. Using the property of square roots, we can simplify this expression as $\sqrt{25} \times \sqrt{2}$, which equals 5$\sqrt{2}$.

Simplifying $\sqrt{20}$

To simplify $\sqrt{20}$, we need to find the largest perfect square that divides 20. The largest perfect square that divides 20 is 4, which is equal to 2 multiplied by 2. We can rewrite $\sqrt{20}$ as $\sqrt{4 \times 5}$, because 20 can be expressed as 4 multiplied by 5. Using the property of square roots, we can simplify this expression as $\sqrt{4} \times \sqrt{5}$, which equals 2$\sqrt{5}$.

Combining the Simplified Expressions

Now that we have simplified both $\sqrt{50}$ and $\sqrt{20}$, we can combine the two expressions to get the final result. We have $\sqrt{50} + \sqrt{20} = 5\sqrt{2} + 2\sqrt{5}$.

Rationalizing the Denominator

In some cases, we may need to rationalize the denominator of a fraction. Rationalizing the denominator involves multiplying the numerator and denominator by a value that eliminates the radical in the denominator. However, in this case, we don't need to rationalize the denominator because the expression is already simplified.

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. In this article, we simplified the expression $\sqrt{50} + \sqrt{20}$ using various mathematical techniques. We found that $\sqrt{50}$ can be simplified as 5$\sqrt{2}$ and $\sqrt{20}$ can be simplified as 2$\sqrt{5}$. Combining the two simplified expressions, we get the final result of 5$\sqrt{2} + 2\sqrt{5}$.

Final Answer

The final answer to the expression $\sqrt{50} + \sqrt{20}$ is 5$\sqrt{2} + 2\sqrt{5}$.

Frequently Asked Questions

• What is the largest perfect square that divides 50? The largest perfect square that divides 50 is 25.
• What is the largest perfect square that divides 20? The largest perfect square that divides 20 is 4.
• How do you simplify $\sqrt{50}$? You can simplify $\sqrt{50}$ as 5$\sqrt{2}$.
• How do you simplify $\sqrt{20}$? You can simplify $\sqrt{20}$ as 2$\sqrt{5}$.
• What is the final answer to the expression $\sqrt{50} + \sqrt{20}$? The final answer to the expression $\sqrt{50} + \sqrt{20}$ is 5$\sqrt{2} + 2\sqrt{5}$.

References

• [1] Khan Academy. (n.d.). Square Roots. Retrieved from https://www.khanacademy.org/math/algebra/x2f-alg-review/x2f-alg-review-roots/x2f-alg-review-sqrt
• [2] Math Open Reference. (n.d.). Square Root. Retrieved from https://www.mathopenref.com/sqrt.html
• [3] Purplemath. (n.d.). Square Roots. Retrieved from https://www.purplemath.com/modules/sqrts.htm

Note: The references provided are for educational purposes only and are not a substitute for professional mathematical advice.

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Introduction

In our previous article, we simplified the expression $\sqrt{50} + \sqrt{20}$ using various mathematical techniques. We found that $\sqrt{50}$ can be simplified as 5$\sqrt{2}$ and $\sqrt{20}$ can be simplified as 2$\sqrt{5}$. Combining the two simplified expressions, we get the final result of 5$\sqrt{2} + 2\sqrt{5}$. In this article, we will answer some frequently asked questions related to the expression $\sqrt{50} + \sqrt{20}$.

Q&A

Q1: What is the largest perfect square that divides 50?

A1: The largest perfect square that divides 50 is 25.

Q2: What is the largest perfect square that divides 20?

A2: The largest perfect square that divides 20 is 4.

Q3: How do you simplify $\sqrt{50}$?

A3: You can simplify $\sqrt{50}$ as 5$\sqrt{2}$.

Q4: How do you simplify $\sqrt{20}$?

A4: You can simplify $\sqrt{20}$ as 2$\sqrt{5}$.

Q5: What is the final answer to the expression $\sqrt{50} + \sqrt{20}$?

A5: The final answer to the expression $\sqrt{50} + \sqrt{20}$ is 5$\sqrt{2} + 2\sqrt{5}$.

Q6: Can you explain the concept of square roots?

A6: 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.

Q7: How do you simplify expressions with square roots?

A7: To simplify expressions with square roots, you need to find the largest perfect square that divides the number inside the square root. You can then rewrite the expression as the product of the square root of the perfect square and the remaining number.

Q8: Can you provide examples of perfect squares?

A8: Yes, here are some examples of perfect squares:

• 1 (1 x 1)
• 4 (2 x 2)
• 9 (3 x 3)
• 16 (4 x 4)
• 25 (5 x 5)

Q9: How do you add and subtract expressions with square roots?

A9: To add and subtract expressions with square roots, you need to combine the like terms. For example, 3$\sqrt{2}$ + 2$\sqrt{2}$ = 5$\sqrt{2}$.

Q10: Can you provide a real-world example of simplifying expressions with square roots?

A10: Yes, here is a real-world example: Suppose you are a carpenter and you need to calculate the length of a diagonal of a square room. The length of the diagonal is given by the expression $\sqrt{2} \times \text{side length}$. If the side length of the room is 5 meters, then the length of the diagonal is $\sqrt{2} \times 5$ meters. Simplifying this expression, we get 5$\sqrt{2}$ meters.

Conclusion

In this article, we answered some frequently asked questions related to the expression $\sqrt{50} + \sqrt{20}$. We provided examples of perfect squares, explained how to simplify expressions with square roots, and provided a real-world example of simplifying expressions with square roots. We hope this article has been helpful in understanding the concept of simplifying expressions with square roots.

Final Answer

The final answer to the expression $\sqrt{50} + \sqrt{20}$ is 5$\sqrt{2} + 2\sqrt{5}$.

References

• [1] Khan Academy. (n.d.). Square Roots. Retrieved from https://www.khanacademy.org/math/algebra/x2f-alg-review/x2f-alg-review-roots/x2f-alg-review-sqrt
• [2] Math Open Reference. (n.d.). Square Root. Retrieved from https://www.mathopenref.com/sqrt.html
• [3] Purplemath. (n.d.). Square Roots. Retrieved from https://www.purplemath.com/modules/sqrts.htm

Note: The references provided are for educational purposes only and are not a substitute for professional mathematical advice.