• Applying SIMPLIFICATION rule for sums such as 454 / (√324 - √225) (√ symbol is square root) Share to Whatsapp



  • Rationalization method is to be used while solving sums like these
    Rationalization factor for :
    1) 1/√a ------> √a
    2) a + √b -------> a - √b
    3) a - √b ---------> a + √b
    4) √a + √b ----------> √a - √b
    5) √a - √b ------------> √a + √b

  • 454 / (√324 - √225)
    As seen in above Rationalization Methods we can use 5th rule to solve the problem
    Thus 454 / (√324 + √225) is multiplied the rationalizing factor i.e. √324 + √225
    To balance the extra added rationlizing factor we multiply the given ratio by √324 + √225 / √324 + √225
    Thus the result of (454 / (√324 - √225)) * (√324 +√225 / √324 + √225) = (454 * (√324 + √225) / ((√324)2 - (√225)2) [ use the identity of (a+b)(a-b) = a2- b2]
    i.e. 454 / √324 - √225 = (454 / √324 - √225) * (√324 +√225 / √324 + √225) = (454 * (√324 + √225) / (324 - 225)
    i.e. 454 / √324 - √225 = (454 / √324 - √225) * (√324 +√225 / √324 + √225) = (454 * (33) / (324 - 225)
    i.e. 454 / √324 - √225 = (454 / √324 - √225) * (√324 +√225 / √324 + √225) = (14982) / (324 - 225)
    i.e. 454 / √324 - √225 = (454 / √324 - √225) * (√324 +√225 / √324 + √225) = (14982) / (99)
    i.e. 454 / √324 - √225 = (454 / √324 - √225) * (√324 +√225 / √324 + √225) = 151.33333333333
    i.e. 454 / √324 - √225 = (454 / √324 - √225) * (√324 +√225 / √324 + √225) = 151 (rounded off to nearest integer)

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