How do you simplify sqrt (18) / (sqrt (8) - sqrt (2))√18√8−√2?

1 Answer
Ben
May 16, 2018

Simplify each radical individually, and then work with the fraction as a whole. You will find that the simplified version is 33

Explanation:

First, we'll simplify the numerator:

sqrt(18)=sqrt(9xx2)√18=√9×2

sqrt(9xx2)=sqrt(9)xxsqrt(2)√9×2=√9×√2

sqrt(9)xxsqrt(2)=3xxsqrt(2)=color(orange)(3sqrt(2)√9×√2=3×√2=3√2

Now the expression can be written as:

color(orange)(3sqrt(2))/(sqrt(8)-sqrt(2))3√2√8−√2

Next, we'll simplify the denominator:

sqrt(8)-sqrt(2)=sqrt(4xx2)-sqrt(2)√8−√2=√4×2−√2

sqrt(4xx2)-sqrt(2)=sqrt(4)xxsqrt(2)-sqrt(2)√4×2−√2=√4×√2−√2

sqrt(4)xxsqrt(2)-sqrt(2)=2xxsqrt(2)-sqrt(2)=2sqrt(2)-sqrt(2)√4×√2−√2=2×√2−√2=2√2−√2

2sqrt(2)-sqrt(2)=(2-1)sqrt(2)=color(blue)(sqrt(2))2√2−√2=(2−1)√2=√2

Re-write the expression again:

color(orange)(3sqrt(2))/color(blue)sqrt(2)3√2√2

Finally, we can simplify the fraction:

(3cancel(sqrt(2)))/cancel(sqrt(2))=color(green)(3)

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
4880 views around the world
You can reuse this answer
Creative Commons License