SOLUTION: ^6√27a^2b^5 x ^6√6a^3b^6

Question 371723: ^6√27a^2b^5 x ^6√6a^3b^6
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

To multiply these we use a property of all radicals: :

which simplifies to:

Next we try to simplify the radical. This is done by finding factors that are powers of 6 (since this is a 6th root). There is one power of 6:

Next we use the property above (this time from right to left) to separate the power of 6:

which simplifies to:

Important: Radical expressions (without a negative sign in front) must not be negative. So our answer should not be negative. Normally one would use absolute value to ensure a non-negative result. However, since the original problem had and since the radicand of a even-numbered root, like 6th roots, must be positive, we know that b could never be negative. So we do not need to be concerned with using absolute value to ensure a non-negative result. If we had not known that b was non-negative, we would have to use

to ensure the final expression is non-negative.
RELATED QUESTIONS
√q+5=6 (answered by stanbon)

Multiply and simplify by factoring √(2b^5 )�√(22c^6 ) Thank you (answered by Alan3354)

5√(2)+6√(8)-7√(45) (answered by RAY100)

1/6a^3b^2(12ab^2-18a^2b+6) (answered by ReadingBoosters)

multiply (8√[6] + 3√[2])(4√[6] � 5√[2]) (answered by Fombitz,stanbon)

Multiply: (8√[6] + 3√[2])(4√[6] � 5√[2])... (answered by MathLover1)

5. Multiply: (√[6] + 2√[2])(4√[6] � 3√[2]) (answered by stanbon)

Multiply (8√[6] + 3√[2])(4√[6] � 5√[2]) (answered by Fombitz)

SOLUTION: ^6&#8730;27a^2b^5 x ^6&#8730;6a^3b^6

SOLUTION: ^6√27a^2b^5 x ^6√6a^3b^6