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√m - √n (√m - √n )× ( √m + √n ) m - n
x x ( √x + √y) x√x + x√y
------------------- = -------------------- = --------------------------
√x - √y (√x - √y)(√x+ √y) x-y
√5 - √2 (√5 - √2) (√5 -√2) 5 -2√10 + 2 7 -2√10
------------ = --------------------------------- = ------------------- = ----------
√5+ √2 (√5 + √2)(√5 -√2) 5-2 3
2√6 - √3 (2√6 - √3 ) (√3 - 2√6) 2√18 - 4 (6) - 3 + 2√18
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√3 + 2√6 (√3 + 2√6) (√3 -2√6) (3) - 4(6)
4√18 - 27
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-21
a + b (a+b)(√a - √b) a√a - a√b +b√a - b√b
--------- = ----------------------- = --------------------------------
√a + √b (√a + √b)(√a - √b) a-b
-5 -5 (2 +√3) -10-5√3
------------- = ----------------------- = ---------------- = -10 -5√3
2 - √3 (2- √3)(2+√3) 4 -3
1 1(3√5 +√2) 3√5 + √2 3√5 + √2
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3√5 -√2 (3√5 -√2)(3√5 +√2 ) 9(5) - 2 43
√2 +3 (√2 +3)(√3 -√2) √6-2 +3√3 -3√2
--------- = -------------------------- = --------------------------- = √6-2 +3√3 -3√2
√3 +√2 (√3 +√2)(√3 -√2) 3-2
.................Kd