A radical is of the form , where p is the index and x is the radicand. It can also be written in terms of powers. For example, it can be written as . It can also be simplified further. 64 = 4 x 4 x 4 = . So, = = = 4.
Example 1: Find the product of 5 and 3
The given radicals are 5 and 3
Here the outside numbers are 5 in 5 and 3 in 3 and inside numbers are 3 and 6 respectively.
Multiply the outside numbers 5 x 3 = 15
Multiply the terms inside the square root = =
Simplify the radical. can be written as = x = 3
Now the product of 5 and 3 is 3.
Example 2: Find the product of , and
Here we cannot multiply the inside numbers directly. Because 5 has a square root, 25 has a cube root and 125 has a 4th root. So inorder to simplify this first we need to find Least Common Multiple of 2, 3, 4. L.C.M = 12.
Now, . . =
When the bases are same, the exponents are added.