3 Ways To Multiply Radicals

Ex. 1: √(18) x √(2) = ? Ex. 2: √(10) x √(5) = ? Ex. 3: 3√(3) x 3√(9) = ?

Ex. 1: √(18) x √(2) = √(36) Ex. 2: √(10) x √(5) = √(50) Ex. 3: 3√(3) x 3√(9) = 3√(27)

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. 1: 3√(2) x √(10) = 3√( ? ) 3 x 1 = 3 Ex. 2: 4√(3) x 3√(6) = 12√( ? ) 4 x 3 = 12

3 x 1 = 3

4 x 3 = 12

Ex. 1: 3√(2) x √(10) = 3√(2 x 10) = 3√(20) Ex. 2: 4√(3) x 3√(6) = 12√(3 x 6) = 12√(18)

3√(20) = 3√(4 x 5) = 3√([2 x 2] x 5) = (3 x 2)√(5) = 6√(5) 12√(18) = 12√(9 x 2) = 12√(3 x 3 x 2) = (12 x 3)√(2) = 36√(2)

The indices are 3 and 2. 6 is the LCM of these two numbers because it is the smallest number that is evenly divisible by both 3 and 2. 6/3 = 2 and 6/2 = 3. To multiply the radicals, both of the indices will have to be 6.

6√(5) x 6√(2) = ?

2 –> 6√(5) = 6√(5)2 3 –> 6√(2) = 6√(2)3

6√(5)2 = 6√(5 x 5) = 6√25 6√(2)3 = 6√(2 x 2 x 2) = 6√8