How do you rationalize the denominator and simplify sqrt(3/2)?

3 Answers
Gió
May 5, 2018

I got as far as this:

Explanation:

Let us write it as:

sqrt(3)/sqrt(2)

multiply and divide by sqrt(2)

sqrt(3)/sqrt(2)color(red)(sqrt(2)/sqrt(2))=(sqrt(3)sqrt(2))/2==sqrt(3*2)/2=sqrt(6)/2

Barney V.
May 5, 2018

sqrt6/2

Explanation:

sqrt (3/2)

:.=sqrt 3/sqrt 2

:.=sqrt 3/sqrt 2xx sqrt 2/sqrt 2

:.=sqrt2xxsqrt2=2

:.=(sqrt(2xx3))/2

:.=sqrt6/2

Jim G.
May 5, 2018

sqrt6/2=1/2sqrt6

Explanation:

"using the "color(blue)"laws of radicals"

•color(white)(x)sqrt(a/b)hArrsqrta/sqrtb

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

•color(white)(x)sqrtaxxsqrta=a

sqrt(3/2)=sqrt3/sqrt2

"to eliminate the radical on the denominator multiply"
"the numerator/denominator by "sqrt2

rArrsqrt3/sqrt2xxsqrt2/sqrt2=(sqrt3xxsqrt2)/(sqrt2xxsqrt2)=sqrt6/2=1/2sqrt6

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
4744 views around the world
You can reuse this answer
Creative Commons License