(√5 + √2) / (√5 - √2) Help! Write in simplified radical form by rationalizing the denominator.?
(√5 + √2) / (√5 - √2) Write in simplified radical form by rationalizing the denominator.
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(√5 + √2) / (√5 - √2) Write in simplified radical form by rationalizing the denominator.
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Verified answer
Multiply the conjugate of denominator
[(√5 + √2) / (√5 - √2)][(√5 + √2)/(√5 + √2)]
(√5 + √2)²/(5 - 2)
(5 + 2 + 2√10)/3
(7 + 2√10)/3
(â5 + â2) / (â5 - â2)
=(â5 + â2) / (â5 - â2) * (â5 + â2) / (â5 + â2) (multiply by 1, with the conjugate of the denominator on both the top and bottom)
=(5 + 2â10 + 2) / (5 - 2)
= (7 + 2â10) / 3
(â5+â2) / (â5-â2)
(â5+â2)(â5+â2) / (â5-â2)(â5+â2)
(5+â10+â10+2) / (5+â10-â10-2)
(7+2â10) / 3
(â5 + â2) / (â5 - â2) = {(â5 + â2) / (â5 - â2)}*{(â5 + â2) / (â5 - â2) }
Multiply and divide by (â5 + â2)
= {(â5 + â2) / (â5 - â2)}*{(â5 + â2) / (â5 + â2) }
= {(â5 + â2)^2 / (5-2) }
= {5+2 +2â10}/3
= (7+2â10)/3 ....................Ans
â5 + â2) / (â5 - â2)
RF(Rationalizing Factor) = â5 + â2
(â5 + â2) (â5 + â2)
-------------- X -----------------
â5 - â2 (â5 + â2)
Multiply Numerators then denominators
â5(â5 + â2) + â2(â5 + â2)
------------------------------------------
â5(â5 + â2) - â2 (â5 + â2)
= â25+â10+â10+â4
------------------------------
â25+â10-â10-â4
= 5 + â20 + 2
----------------------
5 - 2
(The +â10-â10 get cancelled)
= 7+ 2+â20
------------------ -------> Answer
3
Hope it helps!
All the best!
â5 + â2.....â5 + â2..
------------- * -------------- =
â5 - â2......â5 + â2...
(â5 + â2)(â5 + â2)
---------------------------- =
(â5 - â2)(â5 + â2) ........... difference of squares
(â5 + â2)²
--------------- =
â5² - â2²
5 + 2â10 + 2
-------------------- =
.....5 - 2........
7 + 2â10
-------------- <========= the solution
......3.....
P.S.
Ignore the dots, they just keep numbers in place.