Question 94747
The reciprocal means "1 divided by ..." So the reciprocal of the square root of 3 means:
.
{{{1/sqrt(3)}}}
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But convention is that you do not leave a radical (in this case {{{sqrt(3)}}}) in the denominator.
The way you get rid of the square root of 3 is to multiply this fraction by {{{sqrt(3)/sqrt(3)}}}
which is equivalent to multiplying the fraction by 1 because the denominator of the multiplier
is equal to the numerator.
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This multiplication is:
.
{{{(1/sqrt(3))*(sqrt(3)/sqrt(3))= (1*sqrt(3))/(sqrt(3)*sqrt(3)) = sqrt(3)/(sqrt(3)*sqrt(3))}}}
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But in the denominator the multiplication of {{{sqrt(3)*sqrt(3)}}} is equal to {{{3}}}. As a
result the form the answer takes is:
.
{{{sqrt(3)/3}}}
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And this is the conventional form of the reciprocal of the square root of 3.
.
Hope this helps you to explain the problem to your son.