How do you simplify $\frac{\sqrt{3}}{- \sqrt{21}}$ $sqrt3/-sqrt21$ ?

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Answer 1 · 2015-10-12T23:59:37

$- \frac{\sqrt{7}}{7}$ $-sqrt(7)/7$

The firs thing to notice here is that you can write $21$ $21$ as

$21 = 7 \cdot 3$ $21 = 7 * 3$

This means that the denominator of the fraction will be equivalent to

$\sqrt{21} = \sqrt{3 \cdot 7} = \sqrt{3} \cdot \sqrt{7}$ $sqrt(21) = sqrt(3 * 7) = sqrt(3) * sqrt(7)$

SInce $\sqrt{3}$ $sqrt(3)$ is present in both the numerator, and the denominator of the fraction, it will cancel out to give

$sqrt(3)/(-sqrt(21)) = -color(red)(cancel(color(black)(sqrt(3))))/(color(red)(cancel(color(black)(sqrt(3)))) * sqrt(7)) = - 1/sqrt(7)$

Next, rationalize the denominator by multiplying the fraction by $1 = sqrt(7)/sqrt(7)$

$-1/sqrt(7) * sqrt(7)/sqrt(7) = -sqrt(7)/(sqrt(7) * sqrt(7)) = -sqrt(7)/sqrt(7 * 7) = color(green)(-sqrt(7)/7)$

How do you simplify sqrt3/-sqrt21√3−√21sqrt3/-sqrt21?