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How do you multiply radical expressions with different indices?

Answer 1

Kennedy Adams

Determine a common index and make the indices the same.

Example: #sqrt5*root(3)2#

The least common multiple, or 6, is the common index for 2 and 3.

#sqrt5= root(6)(5^3)=root(6)125#

#root(3)2=root(6)(2^2)=root(6)4#

So #sqrt5*root(3)2=root(6)125root(6)4=root(6)(125*4)=root(6)500#

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Answer 2

Genesis Allen

To multiply radical expressions with different indices, you need to simplify each radical expression separately and then multiply them together. First, simplify each radical expression by finding the prime factors of the radicand. Then, group the factors in pairs according to the index of each radical. Finally, multiply the factors within each pair and write the result as a single term under the corresponding radical.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.