Question

Add the following radical expressions where  a > 0 .  √ 36 a + √ 25 a + √ 16 a

Answer 1

All the square roots can be evaluated rationally: √36=6, √25=5, √16=4 so the expression becomes: 6a+5a+4a=15a.

 

Comments

where does the a>0 factor into this equation?

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All it means is that a is positive (non-zero). In actual fact, a can be any value, so we could add the statement that 15a>0 because a>0. The question doesn't ask for the sign of the value of the expression, it just asks us to add the terms. Perhaps it was put in to confuse you!

There is however another explanation. If a is included under the square root (we can't tell) then the answer is 15√a, and so it must be positive for the roots to exist.

If this is the case, the question should have been written more clearly:

√(36a)+√(25a)+√(16a).

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I was getting the same answer as you and kept getting it wrong. However, it was a trick question and should had been written within the () as you mentioned. Tricky! Thanks so much for your help!