How do you simplify #sqrt(7/2)*sqrt(5/3)#?

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Answer 1 · 2017-07-17T14:48:34

See a solution process below:

Use this rule for radicals to simplify the expression:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#sqrt(color(red)(7/2)) * sqrt(color(blue)(5/3)) = sqrt(color(red)(7/2) * color(blue)(5/3)) = sqrt(35/6)#

Or, we can the use this rule of radicals to rewrite the expression:

#sqrt(color(red)(a)/color(blue)(b)) = sqrt(color(red)(a))/sqrt(color(blue)(b))#

#sqrt(color(red)(35)/color(blue)(6)) = sqrt(color(red)(35))/sqrt(color(blue)(6))#

If necessary, we can rationalize the denominator using the following process:

#sqrt(6)/sqrt(6) * sqrt(color(red)(35))/sqrt(color(blue)(6)) =>#

#(sqrt(6) * sqrt(color(red)(35)))/(sqrt(6) * sqrt(color(blue)(6)) =>#

#(sqrt(6 * color(red)(35)))/6 =>#

#sqrt(210)/6#