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Rationalize the denominators of the following:(iii) 1/(√5+√2),(iv) 1/(√7-2) Q.5(iii),(iv)

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Today i am solving the most important question of chapter number system of class 9th ncert . Its very hard to solve the question of exercise 1.5 question 5(iii), (iv) . Sir please help me to solve this tough question in a simplest method.Rationalize the denominators of the following:(iii) 1/(√5+√2),(iv) 1/(√7-2)

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  1. (iii) 1/(√5+√2)

    Solution:

    Multiply and divide 1/(√5+√2) by (√5-√2)

    [1/(√5+√2)]×(√5-√2)/(√5-√2) = (√5-√2)/(√5+√2)(√5-√2)

     

    = (√5-√2)/(√52-√22) [denominator is obtained by the property, (a+b)(a-b) = a2-b2]

    = (√5-√2)/(5-2)

    = (√5-√2)/3

    (iv) 1/(√7-2)

    Solution:

    Multiply and divide 1/(√7-2) by (√7+2)

    1/(√7-2)×(√7+2)/(√7+2) = (√7+2)/(√7-2)(√7+2)

    = (√7+2)/(√72-22) [denominator is obtained by the property, (a+b)(a-b) = a2-b2]

    = (√7+2)/(7-4)

    = (√7+2)/3

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