SOLUTION: Hello, looking for some help with this problem. 5sqrt3(2sqrt15+sqrt8) Thanks!

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Question 1059695: Hello, looking for some help with this problem.

5sqrt3(2sqrt15+sqrt8)

Thanks!

Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
looks to me like you have:

5 * sqrt(3) * (2 * sqrt(15) + sqrt(8))

you would use the distributive law to get:

(5 * sqrt(3) * 2 * sqrt(15)) + (5 * sqrt(3) * sqrt(8))

5 * sqrt(3) * 2 * sqrt(15) is the same as:
5 * 2 * sqrt(3) * sqrt(15) which is the same as:
10 * sqrt(3 * 15) which is the same as:
10 * sqrt(45) which is the same as:
10 * sqrt(9 * 5) which is the same as:
10 * sqrt(9) * sqrt(5) which is the same as:
10 * 3 * sqrt(5) which is the same as:
30 * sqrt(5)

5 * sqrt(3) * sqrt(8) is the same as:
5 * sqrt(24) which is the same as:
5 * sqrt(6 * 4) which is the same as:
5 * sqrt(6) * sqrt(4) which is the same as:
5 * sqrt(6) * 2 which is the same as:
5 * 2 * sqrt(6) which is the same as:
10 * sqrt(6)

your expression of:

(5 * sqrt(3) * 2 * sqrt(15)) + (5 * sqrt(3) * sqrt(8)) becomes:

30 * sqrt(5) + 10 * sqrt(6)

you can evaluate your original expression and your final expression and you will see that they both come up with the same value.

this indicates the simplification process was done correctly.

i did that and got 91.57693675 for both the original expression and the final expressions, which indicates that i did it correctly.

you could factor out a 10 and get 10 * (3 * sqrt(5) + sqrt(6)), but i don't think that would be the simplified answer.

i believe the simplified answer is 30 * sqrt(5) + 10 * sqrt(6).

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

Hello, looking for some help with this problem.

5sqrt3(2sqrt15+sqrt8)

Thanks!

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