Simplifying Radical Expressions. For a radical expression to be simplified it has to satisfy the following conditions: The radicand has no factor raised to a power greater than or equal to the index. (EX:There are no perfect-square factors.) The radicand has no fractions.
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For a radical expression to be simplified it has to satisfy the following conditions:
The radicand has no factor raised to a power greater than or equal to the index. (EX:There are no perfect-square factors.)
The radicand has no fractions.
No denominator contains a radical.
Exponents in the radicand and the index of the radical have nocommon factor, other than one.
*This one can not be simplified any further due to their indexes (2 and 3) being different!
So, the product of two radicals is the radical of their product!
This is really what is taking place, however, we usually don’t show all of these steps! The easiest thing to do is to divide the exponents of the radicand by the index. Any “whole parts” come outside the radical. “Remainder parts” stay underneath the radical.
For instance, 3 goes into 7 two whole times.. Thus will be brought outside the radical. There would be one factor of y remaining that stays under the radical.
Let’s get some more practice!
The index is 2. Square root of 25 is 5. Two goes into 7 three “whole” times, so a
p3is brought OUTSIDE the radical.The remaining p1 is left underneath the radical.
The index is 4. Four goes into 5 one “whole” time, so a
2 and a are brought OUTSIDE the radical. The remaining 2 and a are left
underneath the radical. Four goes into 7 one “whole” time, so b is brought
outside the radical and the remaining b3 is left underneath the radical.
Pythagorean TheoremWhat is the Pythagorean Formula?Quadratic Formula