Multiplication Property of Radicals
When multiplying radicals (with the same index), multiply under the radical, and then multiply in front of the radical (any values multiplied times the radicals).
The multiplication property of radicals states that the product of two or more square roots can be simplified into a single square root if the numbers inside the roots are multiplied together.
For example,
√(4)*√(9) = √(4*9) = √36 = 6
Similarly,
√(16)*√(25)*√(9) = √(16*25*9) = √900 = 30
This property can also be extended to higher order roots:
cuberoot(8)*cuberoot(27) = cuberoot(8*27) = cuberoot(216) = 6
However, it is important to note that this property can only be applied when the roots are the same, that is, both roots are square roots or both roots are cube roots, etc.
Further, we can use this property to simplify more complicated expressions involving radicals, such as,
√(12)*√(27)*√(50) = √(12*27*50) = √(54,000) = 60√15
In this case, we simplify the numbers inside the roots, and then factorize the resulting number to separate its perfect square factors and remaining factors that are products of primes.
Overall, the multiplication property of radicals is a helpful tool in simplifying expressions involving radicals, and aids in performing calculations more efficiently.
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