Rationalize Each Denominator

1. - 8√2 / √5

2. √1/2 x √16/35

3. √16k^6m^4 / √k

4. ^3√t/√25u2

1. rationalize by multiplying top and bottom by the value of the denominator: √5:

(√5)(-8√2) / √5(√5)

-8√10 / √25

-8√10 / 5

can't simplify further




√1/2 x √16/35

is the same as

√ (1/2 x 16/35)

√ (1/1 x 8/35)

√8/35

√8 / √35

rationalize by mutliplying top and bottom by √35:

(√8)(√35) / √(35x35)

(√(4x2))(√35) / √1225

(√4 x √2)(√35) / 35

2(√2 x 35) / 35

2(√70) / 35

can't simplfiy further.





√(16k^6m^4) / √k

[√16 times √k^6 times √m^4] / √k

(4 times k^(6/2) times m^(4/2)) / √k

(4k^3m^2) / ₲k

rationalize by multiplying top and bottom by √k

4k^3m^2√k / √k(√k)

4k^3m^2√k / √k^2

4k^3m^2√k / k

law of exponents; divide the bases, subtract the exponents.

4k^(3-1)m^2√k

4k^2m^2√k

can't simplify further.



assuming expression is

^3√(t) divided by √25u^2

^3√t divided by [₲25 times √u^2]

^3√t divided by (5 times u^(2/2))

^3√t divided by 5u

can't simplify furhter.