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3 years ago

Am I correct on the question above?

Mathematics

1 answer:

Ganezh [65]3 years ago

4 0

Answer:

-3/2 + 1/2 sqrt(5)

Step-by-step explanation:

sqrt(2) - sqrt(10)

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

sqrt(2) + sqrt(10)

To clear the square root in the denominator, we multiply by the conjugate

sqrt(2) - sqrt(10). What we do to the bottom, we do to the top

sqrt(2) - sqrt(10) sqrt(2) - sqrt(10)

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

sqrt(2) + sqrt(10) sqrt(2) - sqrt(10)

sqrt(2) * sqrt(2) -sqrt(2)sqrt(10) -sqrt(2) sqrt(10) +sqrt(10)sqrt(10)

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

sqrt(2) * sqrt(2) -sqrt(2)sqrt(10) +sqrt(2) sqrt(10) - sqrt(10)sqrt(10)

Combining like terms

sqrt(2) * sqrt(2) -2sqrt(2)sqrt(10) -sqrt(2) sqrt(10) + sqrt(10)sqrt(10)

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

sqrt(2) * sqrt(2) - sqrt(10)sqrt(10)

2 - 2 sqrt(20) +10

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

2-10

12 - 2 sqrt(20)

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

-8

sqrt(20) = sqrt(4) sqrt(5) = 2sqrt(5)

Replacing sqrt(20)

12 - 2 *2 sqrt(5)

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

-8

12 -4 sqrt(5)

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

-8

Factor out a 4

4(3 -sqrt(5))

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

4 (-2)

Canceling the 4

3-sqrt(5)

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

-2

Breaking the fraction into 2 pieces

-3/2 + 1/2 sqrt(5)

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