How do you simplify (8sqrt3 )/ sqrt6?

3 Answers
VNVDVI
Mar 27, 2018

8/sqrt(2)

Explanation:

Recall that sqrta/sqrtb=sqrt(a/b)

So, we're looking to simplify 8sqrt(3/6)

3/6=1/2, so we have

8sqrt(1/2)=(8sqrt(1))/sqrt(2)=8/sqrt(2)

Aditya N.
Mar 27, 2018

4 sqrt2

Explanation:

(8 sqrt3)/sqrt6

Rationalize Denominator

(8 sqrt3sqrt6)/6

Combine Roots

(8 sqrt18)/6

Factor

(8 sqrt(9 * 2))/6

Take Out The Nine

(8 * 3 sqrt2)/6

Simplify

(24 sqrt2)/6

Simplify

4 sqrt2

Sridhar V.
Mar 27, 2018

(8 sqrt(3))/(sqrt(6)) = 4 sqrt2

Explanation:

Given:

(8 sqrt(3))/(sqrt(6))

Rationalize the denominator:

rArr (8 sqrt(3))/(sqrt(6))*(sqrt(6))/(sqrt(6))

rArr [8 sqrt(3) sqrt(6)]/(sqrt(6) sqrt(6)

Observe that color(blue)(sqrt(m) * sqrt(m)=m and

rArr color(blue)(sqrt(mn)=sqrt(m)*sqrt(n)

rArr [8 sqrt(3) sqrt(3*2)]/6

rArr (2*4 sqrt(3) sqrt(3) sqrt(2)]/(2*3)

rArr [2*4*3*sqrt(2)]/(2*3)

rArr [cancel (2)*4*cancel 3*sqrt(2)]/(cancel(2)*cancel 3)

rArr 4 sqrt(2)

Hence,

color(red)((8 sqrt(3))/(sqrt(6)) = 4 sqrt2

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