Simplifying multiplied radicals is pretty simple. We use the fact that the product of two radicals is the same as the radical of the product, and vice versa.
The radical symbol (√) represents the square root of a number. You can encounter the radical symbol in algebra or even in carpentry or another trade that involves geometry or calculating relative sizes or distances. You can multiply any two radicals that have the same indices (degrees of a root) together. If the radicals do not have the same indices, you can manipulate the equation until they do. If you want to know how to multiply radicals with or without coefficients
Ex. 1: √(36) = 6. 36 is a perfect square because it is the product of 6 x 6. The square root of 36 is simply 6.
Ex. 2: √(50) = √(25 x 2) = √([5 x 5] x 2) = 5√(2). Though 50 is not a perfect square, 25 is a factor of 50 (because it divides evenly into the number) and is a perfect square. You can break 25 down into its factors, 5 x 5, and move one 5 out of the square root sign to simplify the expression. •You can think of it like this: If you throw the 5 back under the radical, it is multiplied by itself and becomes 25 again.
Ex. 3: 3√(27) = 3. 27 is a perfect cube because it's the product of 3 x 3 x 3. The cube root of 27 is therefore 3.
2: How are radicals multiplied? Show an example to illustrate.
3: What steps do you use to simplify radicals? Give an example, showing each step.