4 Laws of Radicals: Grade 9 Quarter 2

Summary

In this lesson on the laws of radicals, the instructor explains the fundamental properties of radical expressions, such as nth roots and their applications. The video covers the four primary laws: simplifying nth roots, multiplying or dividing radicals, and handling exponents within roots. Through various examples, the instructor demonstrates how to simplify complex expressions involving cube roots, square roots, and other radical forms. The lesson aims to equip students with the skills to simplify and solve radical expressions effectively, using the laws of radicals.

Takeaways

• 😀 The nth root of a raised to 1/n is equivalent to the nth root of a, where n is a positive integer greater than one.
• 😀 The first law of radicals states that the nth root of a raised to n simplifies to a, as the exponent and the root cancel each other out.
• 😀 The second law of radicals explains that the nth root of a times b is the same as the nth root of the product of a and b.
• 😀 The third law of radicals allows the nth root of a divided by the nth root of b to be written as the nth root of the quotient of a and b.
• 😀 The fourth law of radicals states that m times n as the index simplifies as the nth root of a raised to the power of m.
• 😀 Radical expressions can be simplified using these laws, such as the cube root of the 4th root of a, which simplifies to the 12th root of a.
• 😀 In simplifying expressions like the 4th root of x cubed divided by the 4th root of y cubed, it becomes the 4th root of x cubed over y cubed.
• 😀 The cube root of x times the cube root of y simplifies to the cube root of x times y when the index is the same.
• 😀 To simplify expressions like the cube root of 8y^3, it helps to express numbers as powers (e.g., 8 = 2^3), allowing for easier factoring and extraction of the root.
• 😀 In cases involving quotients, such as the cube root of 80g^7 divided by the cube root of 10g^4, simplifications are done by dividing the coefficients and subtracting the exponents of variables.

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