Q&A for How to Multiply Radicals

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.

An index of 4 means the fourth root.

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.

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).

See the wikiHow article Simplify a Square Root .

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...

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.

(5 + 4√3)(5 - 4√3) = [25 - 20√3 + 20√3 - (16)(3)] = 25 - 48 = -23.

Yes, if the indices are the same, and if the negative sign is outside the radical sign.

No, you multiply the coefficient by the root of the radicand.

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.

See Method 3 in the above article.

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.

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.

See Find Nth Roots by Hand or Calculate a Square Root by Hand .

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.)

Multiply the radicands together, and then find the square root of the product. (A radicand is the number inside the radical sign.)

That question is too involved to be answered in this Q&A format. Go to OpenAlgebra.com/2012/11/multiplying-and-dividing-radical.html.

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.