Question 252926
divide and simplify so that there are no radicals in the denominator. show your steps.
1. square root 7 over 100
I will assume the question looks like this:
{{{sqrt(7/100)}}}
we get
{{{sqrt(7) / sqrt(100)}}}
which is
{{{sqrt(7)}}} / {{{10}}}
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2. square root of 18 + square root 24 over square root of 6
({{{sqrt(18)}}} + {{{sqrt(24)}}}) / {{{sqrt(6)}}}
simplify sqrt(18) as 3sqrt(2) and sqrt(24) as 4sqrt(6)
({{{3sqrt(2) + 4sqrt(6)}}}) / {{{sqrt(6)}}}
multiply by conjugate, sqrt(6), on both numerator and denominator to get
({{{3sqrt(2) + 4sqrt(6)}}})*{{{sqrt(6)}}} / {{{6}}}
distribute to get
({{{3sqrt(12) + 4sqrt(36)}}}) / {{{6}}}
simplify the numerator to get
{{{(6sqrt(3) + 24)}}} / {{{6}}}
and then factor out a 6 to get
{{{sqrt(3) + 4}}}.
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3. 8 over square root of 6 
{{{8/sqrt(6)}}}
multiply by conjugate, sqrt(6) on both top and bottom to get
{{{8*sqrt(6) / 6}}}
reduce to get
{{{4sqrt(6)/3}}}