SOLUTION: Tutor please help me simplify {{{ -sqrt( 125 )+3sqrt( 45 ) }}}. I have gotten {{{ -5sqrt( 5 )+3(3sqrt( 5)) }}} and think it is wrong.

Question 897082: Tutor please help me simplify . I have gotten and think it is wrong.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

equation to simplify is -sqrt(125) + 3*sqrt(45)

sqrt(125) is equivalent to sqrt(5*25) which is equal to sqrt(25) * sqrt(5) which is equal to 5*sqrt(5).

sqrt(45) is equivalent to sqrt(5*9) which is equal to sqrt(5) * sqrt(9) which is equal to 3 * sqrt(5)

your original expression of -sqrt(125) + 3*sqrt(45) becomes:

-5 * sqrt(5) + 3 * 3 * sqrt(5). *****

factor out the common factor of sqrt(5) and combine 3*3 to get 9 and your equation becomes:

(-5 + 9) * sqrt(5)

combine like terms to get:

4 * sqrt(5)

if you did this correctly, then:

-sqrt(125) + 3*sqrt(45) should give you the same answer as 4 * sqrt(5)

-sqrt(125) + 3 * sqrt(45) is equal to 8.94427191...

4*sqrt(5) is equal to 8.94427191...

answers are the same, so the final expression is good.

i think you were right, but you didn't finish the job.

you had gotten:

-5 * sqrt(5) + 3 * 3 * sqrt(5)

that looks exactly like what i got at the point marked with *****

that's shown below again for your convenience.

-5 * sqrt(5) + 3 * 3 * sqrt(5). *****

what you got was an intermediate result.

you needed to finish the job by combining like terms and factor out the sqrt(5), etc. as i did above.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Tutor please help me simplify . I have gotten and think it is wrong.

is correct, but since 3(3) = 9, this becomes: , which when combined results in:
(lowest radical form)
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