Question

Rationalize the denominator.

Answer 1

Answer:

7sqrt(15) - 5sqrt(6)

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45

Step-by-step explanation:

7 -sqrt(10)

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

3 sqrt(5) *sqrt(3)

7 -sqrt(10)

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

3 sqrt(15)

Multiply the top and bottom by sqrt(15)/ sqrt(15)

7 -sqrt(10)               sqrt(15)

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

3 sqrt(15)                 sqrt(15)

(7 -sqrt(10))* sqrt(15)

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

3 *15

Distribute

7sqrt(15) - sqrt(150)

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45

sqrt(ab) =sqrt(a) sqrt(b)

150 = 25*6

7sqrt(15) - sqrt(25)sqrt(6)

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45

7sqrt(15) - 5sqrt(6)

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

45

Answer 2

Answer:

21√15 - 15√6 / 135

Step-by-step explanation: First multiply 3√5 with √3 to get 3√15. Then rationalize to get to 21√15 - 3√150 as the numerator. Simplify 3√150 to 15√6, and then you get an answer of 21√15 - 15√6 / 135.