Answer: 120√6
*I apologize for the late response, if any of you need this, I'm happy to help. If the explanation isn't clear, please message me and we can work from there. I have checked this answer 3 times and it has been correct all those three times.*
Question and procedure:
√3 x 2√2 x 5√8 x √18
To solve, first, you should simplify any roots that need simplifying.
The two roots that need simplifying are 5√8 and√18.
In 5√8, you can still simplify the √8, there are four factors of 8: 1,2,4,8. The only two factors that you will be able to further simplify are 2 and 4.
TO SOLVE:
√2 x √4 = 2√2
then, you multiply 2√2 x 5, getting you 10√2
( the root of 4 is 2)
THE OTHER ROOT:
√18: 18 has the following factors: 1,2,3,6,9,18. The two factors that you will be able to further simplify are 9 and 2.
So, √18 is 3√2.
Now we can solve the problem:
√3 x 2√2 x 10√2 x 3√2
( when solving, it is important to keep in mind that you are supposed to multiply the number OUTSIDE the root together and the numbers INSIDE of the root together)
√3 x 2√2 = 2√6.
2√6 x 10√2 = 20 √12
* WE ARE ABLE TO SIMPLIFY 20√12 into 40√3.
40√3 x 3√2 = 120√6.
