How do you simplify #sqrt(1) / sqrt (7) times sqrt(7) / sqrt(11)#?

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Answer 1 · 2016-06-19T07:41:42

#=sqrt11 / 11#

#(sqrt1 / color(blue)(sqrt7)) * (color(blue)(sqrt7) / sqrt11)#

We can observe that #color(blue)(sqrt7# is present in denominator of first term and numerator of second and hence can be cancelled.

# =(sqrt1 / cancelsqrt7) * (cancelsqrt7 / sqrt11)#

#=sqrt1/sqrt11#

Now we rationalise the expression by multiplying the numerator and denominator of the expression by #sqrt11#

#=(sqrt1 * color(blue)(sqrt11))/(sqrt11 * color(blue)(sqrt11)#

#=(sqrt11)/(sqrt (11 *11)#

#=(sqrt11)/(sqrt (11 ^2)#

#=sqrt11 / 11#