Verified answer

You've got to get the radical out of the denominator. This usually means multiplyinng the numerator and denominator by the radical in the denominator

30 / √18 =

30(√18)/ (√18)(√18) =

30√18/18 =

5√18 / 3

5√9 *√2 / 3 =

5*3 √2 / 3

5√2

[by the way, 30 / sqrt(18) = 7.07106781

and 5 sqrt(2) = 7.07106781]

9 / 2 √45 =

9 √ 45 / 2 (√45) (√45) =

9 √ 45 / 2 (45) =

9 √ 45 / 90 =

√ 45 / 10 =

√9 √ 5 / 10 =

3 √5 / 10

[ 9 / (2 sqrt(45)) = 0.670820393 and

3 sqrt(5) / 10 = 0.670820393]

3√6 / √2 =

3√6 √2 / √2 √2 =

3 √12 / 2 =

3 √4 √3 / 2 =

6 √3 / 2 =

3 √3

[(3 sqrt(6)) / sqrt(2) = 5.19615242

and 3 sqrt(3) = 5.19615242,

so, these are all correct]

1)

Step 1: Simplify the root

30 / √18 = 30 / (√9 * √2) = 30/(3√2) = 10/√2

Step 2: Multiply by √2/√2 to move the root to the top, since √x*√x = (√x)^2 = just x

10*√2 / √2*√2 = 10√2/2 = 5√2

2) 9/2√45 = 9/(2*√9*√5) = 9/(6*√5) = 3/(2√5)

3√5 /2√5√5 = (3/10) * √5

3) 3√6 / √2 = √9*√6 / √2 = √54/√2 = √27 = √9*√3 = 3√3 or 3* (√6/√2) = 3*√3

1. multiply the numerator and denominator by the denominator to get rid of the descriminant in the denominator.

ex. 30 / sr of 18 let "sr" be square root

30 * (sr of 18) / sr18 * (sr18)

30 * sr18 / 18

2. factor the square root in the numerator

ex. 30 (sr of 9 * 2) / 18

3. 9 is a perfect square root, so take it out

ex. 30 * 3 * (sr 2) / 18

4. gather like terms

ex. 90 * (sr 2) / 18

5. 90 (sr2) / 18 = 5sr2 = 7.071067812