Answers

2015-10-28T15:11:00+08:00
Just multiply the radicand to a radicand.
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What if the radicals to be multiplied don't have the same index?
Just multiply the index. Then simplify if it can.
  • Brainly User
2015-10-28T16:58:19+08:00
If the radicals have the same index,
a) then,  multiply the coefficients
b) multiply the radicand
c.) Simplify

Example:
(5 \sqrt[3]{x} ) ( \sqrt[3]{ x^{2} } ) ⇒ they have the same index, 3

a)  (5) (1) = 5
b)   (\sqrt[3]{x} )( \sqrt[3]{x ^{2} } ) =  \sqrt[3]{ x^{3} }
c)  The answer is 5 \sqrt[3]{x^{3} } = 5x

If the radicals are not similar, not having same index:
Example:  
( \sqrt[3]{ x^{2} }) ( \sqrt{x ^{3} } )
The first radical has index of 3; the second has 2.

a)  Convert the radical to rational exponents:
     \sqrt[3]{ x^{2} } = x ^{ \frac{2}{3} }
     \sqrt{x ^{3} } = x \frac{3}{2}

b)  Convert fractional exponent to similar fractions; Find their LCD⇒6
     x \frac{2}{3}= x \frac{4}{6}
     x \frac{3}{2}=x \frac{9}{6}

c) Convert to radicals then multiply.  The index for both radicals is 6.
 ( \sqrt[6]{x^{4} } )( \sqrt[6]{x^{9} } ) =  \sqrt[6]{x^{13} }

d)  Simplify:
 \sqrt[6]{x^{13} } = x^{2}  \sqrt[6]{x}

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