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Date:___________________
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High School Mathematics
2.57 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.

Name: ___________________

Date:___________________

High School Mathematics
2.57 Rationalizing Radicals Using its Conjugate

Q 1: Rationalise 13 - 5Ö3 using its conjugate.
86
-94
-86
94

 Q 2: Rationalise 8 + 5Ö3 using its conjugate.
11
-11
21
-21

Q 3: Rationalise 17 + 7Ö3 using its conjugate.
168
-168
-142
142

 Q 4: Rationalise 11 + 2Ö15 using its conjugate.
-45
61
45
-61

Q 5: Rationalise 7 + 4Ö5 using its conjugate.
-42
31
-42
-31

 Q 6: Rationalise 15 + 6Ö5 using its conjugate.
-61
45
-45
61

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 Question 8: This question is available to subscribers only!


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