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In addition/subtraction of radical expressions, combine the radicals with the same index and radicand.  Factor the numerical coefficient of the radicand so that one of the factors can be simplified to its roots.

1.)  \sqrt[5]{2} + 2  \sqrt[]{2}

2.)  4  \sqrt{2}

3.)  (2a ^{2} b+3a ^{3} b ^{2} -1) \sqrt[3]{3b ^{2} }

4.)  (5x-5y) \sqrt{2}

(Please see attached solution)

2 5 2
It's still possible that given are not like terms. Hence keeping the term that is not similar to the other two as it is. Unlike in multiplication of where we can transform the given with different indices to like terms (just like LCD in fractions), then simplify with one index (nth root) :-) Analyzing her handwriting compared to the rest of the radicals, if 5 is not the index, she would write it first touching the line, not hanging. Here, she wrote the symbol first before the index 5 :-)
If she made a mistake, yes, you are right, the answer is 7 square of 2. The level of difficulty where addition and subtraction of unlike radicals are given, is normal. Just like in addition and subtraction of algebraic expressions, not all given are like terms at all times :-)
Peace! :))
Of course, peace :-) There are more complicated problems involving radicals posted here than this one. As I've said you are right if "5" is not an index. you are smart to point that one :-)
**point out that one"
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