Radicación

Summary

The script explains the simplification of the fourth root of the fraction 81/16 using the property of radicals. It shows how to distribute the root between the numerator and denominator, then finds the fourth roots of 81 and 16 by prime factorization. The fourth root of 81 is found to be 3, as 3^4 equals 81, and the fourth root of 16 is 2, since 2^4 equals 16. The final simplified result is 3.

Takeaways

• 📐 The script discusses the simplification of a fourth root fraction.
• 🔢 It applies the property of nth root distribution over fractions.
• 🌿 The script simplifies the fourth root of 81 over 16.
• 🧮 It breaks down the simplification into finding the fourth root of 81 and 16 separately.
• 🔄 The fourth root of 81 is found by prime factorization of 81.
• 📈 The number 81 is factored into 3^4, indicating the fourth root is 3.
• 🔄 The fourth root of 16 is found by prime factorization of 16.
• 📉 The number 16 is factored into 2^4, indicating the fourth root is 2.
• 🏁 The final simplified result of the fourth root of 81 over 16 is 3.
• 📝 The script emphasizes the importance of prime factorization in simplifying roots.

Q & A

What property of radicals is mentioned in the script?

The script mentions the property that the nth root of a fraction a/b is equal to the nth root of a divided by the nth root of b.

What is the expression given in the script to be simplified?

The expression given is the fourth root of 81/16.

How does the script simplify the fourth root of 81/16?

The script simplifies the fourth root of 81/16 by taking the fourth root of the numerator and the denominator separately, resulting in the fourth root of 81 divided by the fourth root of 16.

What is the fourth root of 81?

The fourth root of 81 is 3, because 3 raised to the power of 4 equals 81.

What is the fourth root of 16?

The fourth root of 16 is 2, because 2 raised to the power of 4 equals 16.

How does the script determine the fourth root of 81?

The script determines the fourth root of 81 by prime factorization, finding that 81 is 3 multiplied by itself four times (3^4).

How does the script determine the fourth root of 16?

The script determines the fourth root of 16 by prime factorization, finding that 16 is 2 multiplied by itself four times (2^4).

What is the final simplified result of the expression?

The final simplified result of the expression is 3/2.

What method does the script use to factorize 81 and 16?

The script uses prime factorization to factorize both 81 and 16.

Why is prime factorization useful in this context?

Prime factorization is useful because it helps to identify the base number that, when raised to the power of the root, gives the original number.