SOLUTION: Multiply SQRT(3) (9 SQRT(2)-5 SQRT(25))

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Question 352446: Multiply
SQRT(3) (9 SQRT(2)-5 SQRT(25))
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283%29+%289sqrt%282%29-5sqrt%2825%29%29
Since sqrt%2825%29+=+5 we can replace that square root with a 5:
sqrt%283%29+%289sqrt%282%29-5%2A5%29
which simplifies to:
sqrt%283%29+%289sqrt%282%29-25%29
Now we can multiply, using the Distributive property:
sqrt%283%29%2A9sqrt%282%29-+sqrt%283%29%2A25
In the first part of the above we will use a property of radicals, root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29, to multiply the two square roots:
9sqrt%283%2A2%29-+sqrt%283%29%2A25
which simplifies to:
9sqrt%286%29-+25sqrt%283%29
(Note: sqrt%283%29%2A25 was changed to 25sqrt%283%29 using the Commutative Property of Multiplication. In any term with one or more radicals, it is common practice to use this poperty to move the radical(s) to the back of the term. By having the radical(s) at the end, there is less chance of confusion over what is inside the radical(s) and what is not in the radical(s). For example, sqrt%283%29%2A25 could be confused with sqrt%283%2A25%29, especially when it it written by someone who is not very careful about drawing the radical. With the 25 in front there is no chance anyone could think it was inside the radical.)