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Rationalize the denominator:- (2√5+3√2) / 2√5 - 3√2 |
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Answer» Answer: 19 + 6√10 Step-by-step EXPLANATION: Mutiply both numerator and DENOMINATOR by (2√5+3√2). Now the equation is [(2√5+3√2)^2] / (2√5 - 3√2)*(2√5+3√2) The denominator is of the form (a+b)(a-b) which equals a^2 - b^2. So now the equation is [(2√5+3√2)^2] / [(2√5)^2 - (3√2)^2]. The numerator is of the form (a+b)^2 which equals a^2 + b^2 + 2ab So now it is [(2√5)^2 + (3√2)^2 + 2*2√5*3√2] / [ 20 - 18 ] = { 20 + 18 + 12*√2*√5 ] / 2 = (38 + 12√10) / 2 = (38/2) + [(12√10)/2] = 19 + 6√10 |
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