y, to identify the y 2 as a candidate for release.The x 2 term already has an exponent of 2, but you should rewrite the y 3 term as y 2 The coefficient 18 only has one factor that's a perfect square: 9 so, rewrite 18 as the product 2 Solution: Since this is a square root, you want as much of the radicand as possible to be raised to the second power.It might help to think of ( y 2) 3 as a group of three y 2's, and ( y 2) 3 = y 6 thanks to exponential Rule 3 from Encountering Expressions. Why do you rewrite y 6 as ( y 2) 3 in Example 1(a)? Basically, you're trying to make groups of three things, so that they can be released from the radical. Yank them out in front of the radical, stripping away the third power as they exit the prison, which leaves only 2 and x inside. Of all the pieces in the radicand, only 2 3, x 3, and ( y 2) 3 contain powers of 3.Luckily, y 6 is a perfect cube, since y 2 = y 6, so write it as with that all-important power of 3 as well: ( y 2) 3. x = x 3 + 1 = x 4 so it contains an exponent of 3.Now turn your attention to the variables.2, since 8 is a perfect cube and can be written as 2 3.However, since the index of the radical is 3, you want the factors to be powers of 3 if possible. Solution: Start by factoring the radicand's coefficient in other words, write it as a product of smaller numbers.When asked to simplify radicals, what you're actually doing is paroling the factors within that meet the requirements, and leaving therest inside to rot.Įxample 1: Simplify the radical expressions. So, square roots will only release pieces of its radicand that are raised to the second power, and a radical with an index of 5 will only release things raised to the fifth power. Specifically, a radical will only release things raised to a power that matches its index. However, in order to be released from the radical sign, you must meet its parole requirements. Not all the prisoners are doomed to a life sentence, trapped inside the dank (and foul-smelling) radical big housethere is a chance of parole. Think of a radical symbol like a prison, and the pieces of the radicand as inmates.
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