SOLUTION: Hi, can you please help me with one surd expression and explain the answer to the second surd expression? (I'm sorry if the topic is wrong) Firstly, the questions states, "Expan

Question 854239: Hi, can you please help me with one surd expression and explain the answer to the second surd expression? (I'm sorry if the topic is wrong)
Firstly, the questions states, "Expand and simplify: -3√6 (2√3 - 3√8)." My calculator says the answer is 36√3 - 18√2, yet my answer is always -6√18 - 9√48. I don't understand what I'm doing wrong.
Secondly, I am having trouble understanding this example, "Given that x = 5√2 - 3, find x-1/x." The answer to this question is:
x - 1/x = 5√2 - 3 - 1/5√2-3
= 5√2 - 3 - (5√2 + 3/41)
=(5√2 - 3)/1 * 41/41 - (5√2 +3/41)
= 205√2 - 123 - (5v2 + 3)/41
= 200√2 - 126/41
What I don't understand is where the 41 comes from.
Thank you so much for your help in advanced!
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
Firstly, the questions states, "Expand and simplify: -3√6 (2√3 - 3√8)." My calculator says the answer is 36√3 - 18√2, yet my answer is always -6√18 - 9√48. I don't understand what I'm doing wrong.

-3√6 (2√3 - 3√8).
-6√18+9√48 √18 and √48 further can written 18=3x3x2 squereroot 18= 3√2
√48 =square root of 4x4x3 = 4√3
-6√18+ 9√48 (by putting the value of √18 and √48 )
-6x3√2+9x4√3 =-18√2+36√3
Answer
36√3-18√2
Secondly, I am having trouble understanding this example, "Given that x = 5√2 - 3, find x-1/x." The answer to this question is:
x - 1/x = 5√2 - 3 - 1/5√2-3(by rationalization 5√2+3) than multiplication of (a+b)(a-b)=a^2-b^2 therefor (5√2+3)(5√2-3) =(5√2)^2-(3)^2=50-9=41
further you can do it and understand
= 5√2 - 3 - (5√2 + 3/41)
=(5√2 - 3)/1 * 41/41 - (5√2 +3/41)
= 205√2 - 123 - (5v2 + 3)/41
= 200√2 - 126/41

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