How do you simplify #sqrt75/sqrt3#?

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Answer 1 · 2018-07-29T11:00:04

#+-5#

#"using the "color(blue)"law of radicals"#

#•color(white)(x)sqrta/sqrtbhArrsqrt(a/b)#

#sqrt75/sqrt3=sqrt(75/3)=sqrt25=+-5#

Answer 2 · 2018-07-29T18:02:28

#pm5#

We can rewrite #sqrt75# as #sqrt25sqrt3#. We now have:

#(sqrt25sqrt3)/sqrt3#

We can cancel out common factors in the numerator and denominator to get

#(sqrt25cancelsqrt3)/cancelsqrt3=sqrt25=pm5#

Another way to approach this is leveraging the radical law

#sqrta/sqrtb=sqrt(a/b)#. With this in mind, we can rewrite this entire expression as

#sqrt(75/3)=sqrt25=+-5#

Hope this helps!