Q&A for How to Multiply Radicals

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  • Question
    How do I multiply a radical by a whole number?
    Jake Adams
    Academic Tutor
    Jake Adams is an academic tutor and the owner of Simplifi EDU, a Santa Monica, California based online tutoring business offering learning resources and online tutors for academic subjects K-College, SAT & ACT prep, and college admissions applications. With over 14 years of professional tutoring experience, Jake is dedicated to providing his clients the very best online tutoring experience and access to a network of excellent undergraduate and graduate-level tutors from top colleges all over the nation. Jake holds a BS in International Business and Marketing from Pepperdine University.
    Academic Tutor
    Expert Answer
    So, you have two options: simplify the radical as much as possible, and then multiply the number outside the radical by any other number in the multiplication, leaving your answer in radical form. Alternatively, if you prefer a decimal result, you can multiply the number by the decimal approximation of the radical expression. These are the two methods that come to mind because it would depend on your formula, solution, or goal.
  • Question
    What does index of 4 mean?
    Donagan
    Top Answerer
    An index of 4 means the fourth root.
  • Question
    Can I multiply a number inside the radical with a number outside the radical?
    Community Answer
    Only if you are reversing the simplification process. For example, 3 with a radical of 8. 3 squared is 9, so you multiply 9 under the radical with the eight for the original. It would be 72 under the radical.
  • Question
    Can you multiply radicals with the same bases but indexes?
    Orangejews
    Community Answer
    Yes, though it's best to convert to exponential form first. To multiple squareroot2 by cuberoot2, write it as 2^(1/2)*2^(1/3) . Then the rules of exponents make the next step easy as adding fractions: = 2^((1/2)+(1/3)) = 2^(5/6).
  • Question
    How would I use the root of numbers that aren't a perfect square?
    Donagan
    Top Answerer
    See the wikiHow article Simplify a Square Root .
  • Question
    What's the difference between an arithmetic sequence and geometric sequence?
    Donagan
    Top Answerer
    In an arithmetic sequence each number (after the first) is derived by adding a particular number to the previous number in the sequence, as in 2, 4, 6, 8, 10... In a geometric sequence each number (after the first) is derived by multiplying the previous number by a common multiplier, as in 2, 6, 18, 54...
  • Question
    How do you multiply a coefficient and a radical by a radical?
    Community Answer
    Multipy the radicals together, then place the coeffcient in front of the result. For example, to multiply 2√2 and √3, first multiply √2 and √3 to get √6, then put the coeffcient of 2 in front to get 2√6.
  • Question
    How would I multiply (5 + 4√3)(5 - 4√3)?
    Donagan
    Top Answerer
    (5 + 4√3)(5 - 4√3) = [25 - 20√3 + 20√3 - (16)(3)] = 25 - 48 = -23.
  • Question
    Can I multiply a negative radical with a positive radical?
    Donagan
    Top Answerer
    Yes, if the indices are the same, and if the negative sign is outside the radical sign.
  • Question
    Can you multiply the coefficient and the radicand?
    Donagan
    Top Answerer
    No, you multiply the coefficient by the root of the radicand.
  • Question
    Shouldn't the fractions in method 3, step 1 be 6/3 and 6/2, not 3/6 and 2/6?
    Community Answer
    The text for that step is OK for finding LCM, but the picture is wrong and needs to be remade. It is never correct to write 3/6 = 2.
  • Question
    How do I multiply radicals with different indexes?
    Donagan
    Top Answerer
    See Method 3 in the above article.
  • Question
    Is the coefficient different from the index?
    Donagan
    Top Answerer
    Yes. The coefficient is a number appearing in front of the radical sign and being multiplied by the radical. The index is the small number shown within the front angle of the radical sign representing the root being applied to the radicand.
  • Question
    How do you know what power to raise both sides of an equation to if the indices of the radicals are different?
    Community Answer
    Try the least common multiple of the indices. If you have something like square root of x = 5th root of y, then raise both to the 10th power to get rid of all the radicals and reduce to x^5 = y^2.
  • Question
    How do I find the root of a number?
    Donagan
    Top Answerer
  • Question
    What is a radical number?
    Donagan
    Top Answerer
    It is a specific root of some other number. It could be a square root, a cube root, a fourth root or some other root. Examples are the square root of 6, the cube root of 120, the fourth root of 45.5 and the fifth root of 75,699. Those are all radicals when expressed with a root symbol (√). (That is, √6 is a radical number, but the equivalent 2.449 is not.)
  • Question
    How do I multiply square root radicals?
    Donagan
    Top Answerer
    Multiply the radicands together, and then find the square root of the product. (A radicand is the number inside the radical sign.)
  • Question
    How do you divide radicals?
    Donagan
    Top Answerer
    That question is too involved to be answered in this Q&A format. Go to OpenAlgebra.com/2012/11/multiplying-and-dividing-radical.html.
  • Question
    How do I check when multiplying mixed radicals?
    I_l1ke_gam3s
    Community Answer
    Be careful when doing it, and remember you can only multiply radicals like root x times root y = root xy if only one of them are positive.
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