solve this.
12/ (3+√5+2√2)
Answers
Answer:
1 + √5 + √2 - √10
Step-by-step explanation:
To rationalize the denominator of 12/3+√5+2√2, multiply its denominator & numerator by the Rationalizing factor {3 - (√5+2√2)} as shown below :
=> 12 3 - (√5+2√2)
--------------------- x ------------------------
3 + (√5+2√2) 3 - (√5+2√2)
= 36 - 12 (√5 + 2√2)
-------------------------------
9 - (√5+2√2)²
= 36-12 (√5+2√2)
-----------------------------
9 - (5 + 8 + 4√10)
= - {9-3 (√5+2√2)} √10-1
------------------------- x -------------
√10+1 √10-1
= {3(√5+2√2) - 9} (√10-1)
--------------------------------------
10-1
= 3√50 - 3√5 + 6√20 - 6√2 - 9√10 + 9
--------------------------------------------------------
9
= 15√2 - 3√5 + 12√5 - 6√2 - 9√10 + 9
--------------------------------------------------------
9
= 9√2 + 9√5 - 9√10 + 9
--------------------------------------
9
= √2 + √5 - √10 + 1
Rewriting the above value as:
= 1 + √5 + √2 - √10