What Is 48 \sqrt{48} 48 ​ In Simplified Form?A. 4 3 4 \sqrt{3} 4 3 ​ B. 2 12 2 \sqrt{12} 2 12 ​ C. 24D. 48 \sqrt{48} 48 ​ Can't Be Simplified.

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Understanding the Concept of Simplifying Square Roots

When dealing with square roots, simplifying them is an essential skill to master in mathematics. A square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 16 is 4 because 4 multiplied by 4 equals 16. However, not all square roots can be simplified, and in this article, we will explore the simplified form of $\sqrt{48}$.

The Process of Simplifying Square Roots

To simplify a square root, we need to find the largest perfect square that divides the number inside the square root. This can be achieved by factoring the number into its prime factors. Once we have the prime factors, we can identify the perfect squares and take their square roots. The remaining factors will be left inside the square root.

Simplifying $\sqrt{48}$

To simplify $\sqrt{48}$, we need to find the prime factors of 48. The prime factorization of 48 is $2^4 \times 3$. Now, we can identify the perfect square, which is $2^2 = 4$. We can take the square root of 4, which is 2. So, we can rewrite $\sqrt{48}$ as $\sqrt{2^4 \times 3} = \sqrt{4 \times 2^2 \times 3} = 2\sqrt{2^2 \times 3} = 2\sqrt{12}$.

Evaluating the Options

Now that we have simplified $\sqrt{48}$ to $2\sqrt{12}$, we can evaluate the options given in the discussion category.

• Option A: $4\sqrt{3}$ is not the simplified form of $\sqrt{48}$.
• Option B: $2\sqrt{12}$ is the simplified form of $\sqrt{48}$.
• Option C: 24 is not the simplified form of $\sqrt{48}$.
• Option D: $\sqrt{48}$ can be simplified, and we have found its simplified form.

Conclusion

In conclusion, the simplified form of $\sqrt{48}$ is $2\sqrt{12}$. This can be achieved by finding the prime factors of 48, identifying the perfect square, and taking its square root. The remaining factors will be left inside the square root. This skill is essential in mathematics, and it will help us simplify square roots in various problems.

Frequently Asked Questions

Q: What is the simplified form of $\sqrt{48}$?

A: The simplified form of $\sqrt{48}$ is $2\sqrt{12}$.

Q: How do we simplify square roots?

A: To simplify a square root, we need to find the largest perfect square that divides the number inside the square root. This can be achieved by factoring the number into its prime factors. Once we have the prime factors, we can identify the perfect squares and take their square roots. The remaining factors will be left inside the square root.

Q: What is the prime factorization of 48?

A: The prime factorization of 48 is $2^4 \times 3$.

Q: How do we identify the perfect square in the prime factorization of 48?

A: We can identify the perfect square by looking for pairs of the same prime factor. In the prime factorization of 48, we have $2^4$, which has two pairs of 2. We can take the square root of 4, which is 2.

Final Thoughts

Simplifying square roots is an essential skill in mathematics, and it will help us solve various problems. By understanding the concept of simplifying square roots, we can simplify square roots in various problems. In this article, we have simplified $\sqrt{48}$ to $2\sqrt{12}$, and we have evaluated the options given in the discussion category. We hope that this article has provided value to readers and has helped them understand the concept of simplifying square roots.

Understanding the Concept of Simplifying Square Roots

Simplifying square roots is an essential skill in mathematics, and it will help us solve various problems. In this article, we will answer some frequently asked questions about simplifying square roots.

Q&A Session

Q: What is the simplified form of $\sqrt{48}$?

A: The simplified form of $\sqrt{48}$ is $2\sqrt{12}$.

Q: How do we simplify square roots?

A: To simplify a square root, we need to find the largest perfect square that divides the number inside the square root. This can be achieved by factoring the number into its prime factors. Once we have the prime factors, we can identify the perfect squares and take their square roots. The remaining factors will be left inside the square root.

Q: What is the prime factorization of 48?

A: The prime factorization of 48 is $2^4 \times 3$.

Q: How do we identify the perfect square in the prime factorization of 48?

A: We can identify the perfect square by looking for pairs of the same prime factor. In the prime factorization of 48, we have $2^4$, which has two pairs of 2. We can take the square root of 4, which is 2.

Q: Can we simplify $\sqrt{50}$?

A: Yes, we can simplify $\sqrt{50}$. The prime factorization of 50 is $2 \times 5^2$. We can identify the perfect square, which is $5^2 = 25$. We can take the square root of 25, which is 5. So, we can rewrite $\sqrt{50}$ as $\sqrt{2 \times 5^2} = 5\sqrt{2}$.

Q: Can we simplify $\sqrt{64}$?

A: Yes, we can simplify $\sqrt{64}$. The prime factorization of 64 is $2^6$. We can identify the perfect square, which is $2^4 = 16$. We can take the square root of 16, which is 4. So, we can rewrite $\sqrt{64}$ as $\sqrt{2^6} = 4\sqrt{2^2} = 4\sqrt{4} = 4 \times 2 = 8$.

Q: Can we simplify $\sqrt{75}$?

A: Yes, we can simplify $\sqrt{75}$. The prime factorization of 75 is $3 \times 5^2$. We can identify the perfect square, which is $5^2 = 25$. We can take the square root of 25, which is 5. So, we can rewrite $\sqrt{75}$ as $\sqrt{3 \times 5^2} = 5\sqrt{3}$.

Q: Can we simplify $\sqrt{81}$?

A: Yes, we can simplify $\sqrt{81}$. The prime factorization of 81 is $3^4$. We can identify the perfect square, which is $3^2 = 9$. We can take the square root of 9, which is 3. So, we can rewrite $\sqrt{81}$ as $\sqrt{3^4} = 3\sqrt{3^2} = 3\sqrt{9} = 3 \times 3 = 9$.

Conclusion

In conclusion, simplifying square roots is an essential skill in mathematics, and it will help us solve various problems. By understanding the concept of simplifying square roots, we can simplify square roots in various problems. In this article, we have answered some frequently asked questions about simplifying square roots, and we hope that this article has provided value to readers.

Final Thoughts

Simplifying square roots is an essential skill in mathematics, and it will help us solve various problems. By understanding the concept of simplifying square roots, we can simplify square roots in various problems. We hope that this article has provided value to readers and has helped them understand the concept of simplifying square roots.

Additional Resources

• Simplifying Square Roots
• Prime Factorization
• Square Roots

Related Articles

• What is the Simplified Form of $\sqrt{48}$?
• How to Simplify Square Roots
• Prime Factorization of 48

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