simplify 4 cube root 81 - 8 3 Cube root 343 +15 5 cube root 32+root 225
Answers
When multiplying radical expressions with the same index, we use the product rule for radicals. If a and b represent positive real numbers,
Example 1: Multiply: √2⋅√6
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Solution: This problem is a product of two square roots. Apply the product rule for radicals and then simplify.
Answer: 2√3
Example 2: Multiply: 3√9⋅3√6
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Solution: This problem is a product of cube roots. Apply the product rule for radicals and then simplify.
Answer: 33√2
Often there will be coefficients in front of the radicals.
Example 3: Multiply: 2√3⋅5√2
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Solution: Using the product rule for radicals and the fact that multiplication is commutative, we can multiply the coefficients and the radicands as follows.
Typically, the first step involving the application of the commutative property is not shown.
Answer: 10√6
Example 4: Multiply: −23√5x⋅33√25x2
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Solution:
Answer: −30x
Use the distributive property when multiplying rational expressions with more than one term.
Example 5: Multiply: 4√3(2√3−3√6)
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Solution: Apply the distributive property and multiply each term by 4√3
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Answer: 24−36√2