Question 72254
The problem is to simplify:
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{{{sqrt(5)}}} divided by {{{sqrt(2*b)}}}
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Let's first show the division of these two terms:
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{{{(sqrt(5))/(sqrt(2*b))}}}
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But it is normally considered bad form to leave a radical in the denominator.  Therefore,
let's multiply this entire expression by {{{(sqrt(2*b))/(sqrt(2*b))}}}.
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You may notice that this multiplier equals 1 because the numerator and denominator are identical.
So by multiplying this times the original problem we are just multiplying the problem
by an expression that equals 1.
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This gives us:
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{{{((sqrt(5))/(sqrt(2*b)))*((sqrt(2*b))/(sqrt(2*b))) }}}
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which combines to:
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{{{(sqrt(5)*sqrt(2*b))/(sqrt(2*b)*sqrt(2*b))}}}
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The product in the denominator is {{{sqrt(2*b)*sqrt(2*b)}}} and it equals {{{2*b}}}. 
So the expression becomes:
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{{{(sqrt(5)*sqrt(2*b))/(2*b)}}}
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But by the rules of radical operations the product of the two terms in the numerator 
can be combined under a single radical sign to give:
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{{{sqrt(5*2*b)/(2*b)}}}
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and finally multiply the two terms inside the radical sign to get:
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{{{sqrt(10*b)/(2*b)}}}
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This is an acceptable answer, but if you prefer, you can also write it as:
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{{{(1/(2*b))*sqrt(10*b)}}}
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Hope this helps you to understand the processes involved in messing around with radicals.