Addition and Subtraction of Surds

Surds in their basic forms which are similar can be added or subtracted.

Example:  Evaluate the following

(a)√32 + 3√8       (b) 7√3 – √75      (c) 3√48 – √75 + 2√12

Solution

• (√32  + 3√8

=√ (16 x 2) + 3√ (4 x 2)

=4√2 + 6√2

= 10√2

(b) 7√3 – √75

= 7√3 – √ (25 x 3)

=7√3 – 5√3

=2√2

(c) 3√48 – √75 + 2√12

= 3√ (16 x 3) – √ (25 x 3) + 2√ (4 x 3)

= 12√3 – 5√3 + 4√3

= 11√3

EVALUATION (USE THE BOX AT THE BOTTOM TO POST YOUR ANSWER FOR DISCUSSION AND APPRAISAL)

1. Simplify the following (a)5 √ 12 – 3 √ 18  +  4 √72  + 2  √75 (b) 3√2  – √32  + √50 + √98
2. Multiply the following by their conjugate (a) √3 -2√5 (b) 3√2 + 2√3