How do you simplify sqrt 8 /( 2 sqrt3)√82√3?

3 Answers
Meave60
Feb 28, 2016

(sqrt8)/(2sqrt 3)=color(blue)((sqrt 6)/3)√82√3=√63

Explanation:

(sqrt 8)/(2sqrt 3)√82√3

Simplify sqrt 8√8.

sqrt 8=sqrt(2xx2xx2)=sqrt(2^2xx 2)=2sqrt2√8=√2×2×2=√22×2=2√2

Rewrite the fraction.

(2sqrt2)/(2sqrt 3)2√22√3

Rationalize the denominator by multiplying the numerator and denominator by sqrt 3√3.

(2sqrt2)/(2sqrt 3)xx(sqrt3)/(sqrt 3)2√22√3×√3√3

Simplify.

(2sqrt2sqrt3)/(2xx3)2√2√32×3

Simplify.

(2sqrt6)/(2xx3)2√62×3

Simplify.

(cancel2sqrt6)/(cancel2xx3)

Simplify.

(sqrt 6)/3

Chaven Y.
Feb 28, 2016

sqrt (2/3)

Explanation:

8=2^3
sqrt (8) = 2^(3/2)

Therefore we have

(2^(3/2).2^(-1))/sqrt (3)

Add the exponent coefficients for 2

(2^(1/2))/sqrt (3)

Same as sqrt(2/3)

Veddesh phi
Feb 28, 2016

sqrt(2/3)

Explanation:

sqrt8/(2sqrt3)

We could see that

sqrt8=sqrt(4*2)

So

=sqrt(4*2)/(2sqrt3_

=(cancel2sqrt2)/(cancel2sqrt3)

=sqrt2/sqrt3=sqrt(2/3)

But wait ! We could not have irrational numbers in the denominator.

So,rationalize the denominator by multiplying with sqrt3/sqrt3

sqrt2/sqrt3*sqrt3/sqrt3

=sqrt6/3

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