SOLUTION: 2. simplify the following expression by rationalizing the denominator: 5square root of 2 over(/) 4 square root of 3 - the square root of 5

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Question 37758: 2. simplify the following expression by rationalizing the denominator:


5square root of 2 over(/) 4 square root of 3 - the square root of 5
Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
If I am correct you would like to simplify the following expression by rationalization...
+%285%2Asqrt%28+2%29%29%2F+%284%2Asqrt+%283%29-+sqrt+%285%29%29+
To rationalize this expression we need to multiply both the numerator and the denominator by the conjugate of the denominator.
So it looks like this...
+%28%285%2Asqrt%28+2%29%29%2F+%284%2Asqrt+%283%29-+sqrt+%285%29%29%29++%28%284%2Asqrt+%283%29%2B+sqrt+%285%29%29%2F+%284%2Asqrt+%283%29%2B+sqrt+%285%29%29%29+
Then foil the numerator and the denominator...
+%2820%2Asqrt+%286%29+%2B+5%2Asqrt+%2810%29%29%2F+%2816%2Asqrt+%289%29-+sqrt+%2825%29%29+
Which can be simplified...
+%2820%2Asqrt+%286%29+%2B+5%2Asqrt+%2810%29%29%2F+%2816%2A3+-+5%29%29+
And...
+%2820%2Asqrt+%286%29+%2B+5%2Asqrt+%2810%29%29%2F+%2843%29%29+
And this expression cannot be simplified any further.
I hope this helps.
Good Luck!