Algebra

Rationalize each expression by building perfect nth root factors for each denominator. Assume all variables represent positive quantities. I don’t understand how to compute these. Also I don’t have the square root sign so I typed it out where it would be and the number before or after.

1. -4/Square root 20
2. Square root of 125/12n^3

3. Square root 10-3 /Square root 3 +Square root 2

4. 7+ square root 6 /3-3 square root 2

1. -4/√20 = -4√20/20 = -1/5 √20 = -2/5 √5

√(125/n^3) = √(25/n^2) √(5/n) = 5/n √(5/n)
= 5/n √(5n/n^2) = 5/n^2 √(5n)

(√10-3)/(√3+√2)
= (√10-3)(√3-√2) / (3-2)
= √30-3√3-√20+3√2
= 3√2-3√3-2√5+√30

(7+√6)/(3-√2)
= (7+√6)(3+√2) / (9-2)
= (21+3√6+7√2+√12)/7
= 1/7 (21 + 3√6 + 7√2 + 2√3)

posted by Steve
2. 8*/81-6/16

posted by corrine
3. 1/3 + 3/x 1/9 - 9/x square

posted by Nocholas

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