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### High School Mathematics2.57 Rationalizing Radicals Using its Conjugate

 If the product of two mixed surds a + Öb and a - Öb, where a and b are rational numbers is a rational number. then a + Öb and a - Öb are called conjugate radicals. Example: Rationalize 8 + 3Ö5 using its conjugate. Solution: The conjugate of 8 + 3Ö5 is 8 - 3Ö5 Therefore, rationalising factor of 8 + 3Ö5 is 8 - 3Ö5 Rationalising 8 + 3Ö5 with its conjugate, we get (8 + 3Ö5)(8 - 3Ö5) = 64 - 9*5 = 64 - 45 = 19 Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: Rationalise 8 + 5Ö3 using its conjugate.-1111-2121 Q 2: Rationalise 8 - 2Ö15 using its conjugate.-446-6 Q 3: Rationalise 17 + 7Ö3 using its conjugate.142-168168-142 Q 4: Rationalise 7 + 4Ö5 using its conjugate.31-31-42-42 Q 5: Rationalise 11 + 2Ö15 using its conjugate.-45-616145 Q 6: Rationalise 15 + 6Ö5 using its conjugate.4561-61-45 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!