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[drpharMD]

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[(15)^(1/2)] x [(3)^(1/2)] / [(10)^(1/2)] = 3 x (2)^(1/2) / 2. How?

 

[262912]

[(15)^(1/2)] x [(3)^(1/2)] / [(10)^(1/2)] = 3 x (2)^(1/2) / 2. How?

This probably should be posted in the DAT section, but here's an explanation...

(√15 * √3) / √10 --combine the top terms
= √45 / √10 --factor 45 into 3*3*5 and 10 into 2*5
= √(3*3*5) / √(2*5) --move the 3*3 out of the square root since √3*√3=√9=3
= 3√5 / (√2*√5) --the √5 cancel out on top and bottom
= 3 / √2 --multiply the top and bottom by √2
= 3√2 / 2

 

[drpharMD]

Nice! Thanks -- but why multiply the bottom and top by (2)^(1/2)?

 

[262912]

Nice! Thanks -- but why multiply the bottom and top by (2)^(1/2)?

so you don't have a radical in the denominator

 

[allstardentist]

i think this thread belongs to DAT section

 

[NyCzPeter]

ANother way is combine the terms into √45/√10

Pull out a 3 to make 3 x √5/√10 Combine the two radicals into one fraction under one radical
Simplify the √(5/10) into √(1/2)

So you end up with 3 x 1/√2 then multiply top and bottom of fraction by √2 and u get the answer