How do you simplify \frac { 9} { \sqrt { 21} }9√21?

3 Answers
Chad
Apr 3, 2017

27/7277

Explanation:

Firstly, we have to get rid of the radical. To do that, we can ^2^2(square) the entire fraction and then solve from there.

(9/sqrt21)^2=(9*9)/(sqrt21)^2=81/21(9√21)2=9⋅9(√21)2=8121 ~(3 can be taken out)~ =27/7=277

Jim G.
Apr 3, 2017

(3sqrt21)/73√217

Explanation:

To eliminate the sqrt21√21 from the denominator of the fraction we use a method called color(blue)"rationalising"rationalising

This ensures that we have a color(blue)"rational"rational denominator as opposed to a color(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 by sqrt21√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

Barney V.
Apr 5, 2017

color(red)(=(3sqrt21)/7

Explanation:

9/sqrt21

:.=3^2/(sqrt3 xx sqrt7)

:.=3^2/(3^(1/2)sqrt7)

:.=3^(2-1/2)/sqrt7

:.=(3^(1 1/2))/(sqrt7)

:.=3^(3/2)/sqrt7

:.=root2(3^3)/sqrt7

:.=sqrt(3^3)/sqrt7

Rationalize denominator by multiplying by sqrt7/sqrt7

:.=(sqrt(3^3))/sqrt7 xx sqrt7/sqrt7

:.=sqrt3*sqrt3=3,sqrt7*sqrt7=7

:.=sqrt(3*3*3*7)/7

:.=(3sqrt(3*7))/7

:.color(red)(=(3sqrt21)/7

Related questions
Impact of this question
2195 views around the world
You can reuse this answer
Creative Commons License