Understanding Radical Multiplication

The video tutorial explains how to multiply two radicals with different indexes by first converting them into rational exponents. It emphasizes the importance of having a common index to perform multiplication. The process involves finding a common denominator for the exponents, rewriting the expressions back into radical form, and then performing the multiplication. The tutorial concludes by calculating the final product and checking if it can be simplified further.

Why is it necessary to have the same index when multiplying two radicals?

• To convert them into fractions

• To simplify the radicals to integers

• To allow the radicands to be multiplied

• To ensure the coefficients can be added

What is the first step in finding a common index for radicals with different indexes?

• Convert the radicals to decimals

• Use rational exponents

• Add the indexes together

• Multiply the radicands

How do you find a common denominator for the exponents 1/2 and 1/3?

• Multiply both by 6

• Add the fractions

• Find the least common multiple

• Subtract the smaller from the larger

What is the result of rewriting 2^(1/2) and 3^(1/3) with a common denominator?

• 2^(3/6) and 3^(2/6)

• 2^(1/3) and 3^(1/2)

• 2^(2/3) and 3^(3/2)

• 2^(1/6) and 3^(1/6)

What is the next step after obtaining a common index for the radicals?

• Divide the radicands

• Convert back to radical form

• Multiply the coefficients

• Add the exponents

What is the sixth root of 2 cubed?

• The fourth root of 16

• The sixth root of 8

• The cube root of 2

• The square root of 8

What is the sixth root of 3 squared?

• The fourth root of 81

• The square root of 9

• The cube root of 3

• The sixth root of 9

What is the final product of multiplying the sixth roots of 2 cubed and 3 squared?

• The sixth root of 72

• The square root of 72

• The cube root of 72

• The fourth root of 72

Why does the sixth root of 72 not simplify further?

• It has no equal factors

• It is already in simplest form

• It is a prime number

• It is an irrational number

What is the equivalent expression for the product of square root 2 and cube root 3?

• The fourth root of 72

• The sixth root of 72

• The cube root of 72

• The square root of 72