How do you simplify \frac { 9} { \sqrt { 21} }9√21?
3 Answers
Explanation:
Firstly, we have to get rid of the radical. To do that, we can
Explanation:
To eliminate the
sqrt21√21 from the denominator of the fraction we use a method calledcolor(blue)"rationalising"rationalising This ensures that we have a
color(blue)"rational"rational denominator as opposed to acolor(blue)"surd".surd. Consider
sqrt100xxsqrt100√100×√100
sqrt100=10√100=10
rArrsqrt100xxsqrt100⇒√100×√100
=10xx10=10×10
=100larrcolor(red)" the value inside the root"=100← the value inside the root
"in general " sqrtaxxsqrta=ain general √a×√a=a
"Since " 9/sqrt21" is a fraction"since 9√21 is a fraction we multiply the numerator/denominator bysqrt21√21
rArr9/sqrt21xxsqrt21/sqrt21⇒9√21×√21√21
=(9xxsqrt21)/21larrcolor(red)" using above result"=9×√2121← using above result
=(cancel(9)^3xxsqrt21)/cancel(21)^7larrcolor(red)" cancelling by 3"
=(3sqrt21)/7
Explanation:
Rationalize denominator by multiplying by