Question

How can you write the expression with a rationalized denominator? 5-√2/√3

Answer 1

1/3 (5sqrt(3) - sqrt(6))

Explanation:

To rationalize the denominator, we need to get rid of the square root.

We multiply by the square root and it will become a whole number.

5 - sqrt(2)

--------------

sqrt(3)

Multiply the top and bottom by sqrt(3)

5 - sqrt(2) sqrt(3)

-------------- * -----------

sqrt(3) sqrt(3)

Distribute the sqrt(3) on top

5sqrt(3) - sqrt(2) sqrt(3)

-------------------------

sqrt(3) * sqrt(3)

5sqrt(3) - sqrt(6)

-------------------------

3

Rewriting

1/3 (5sqrt(3) - sqrt(6))

Answer 2

(5 - √2) / √3

Multiply the fraction by √3 / √3:

((5 - √2) * √3) / (√3 *√3)

Simplify to get (5√3 - √6) / 3