Surds

Question 1

Simplifying

Answer 1

Divide by largest possible perfect square

Root 32 = root16 x root2
= 4 x root2
= 4root2

5Root40 = 5 x root4 x root10
——————
6

            = 5 x 2 x root10
               --------------
                          6

            = 10root10
              ---------
                    6

            = 5root10
               --------
                    3

Question 2

Adding or subtracting

Answer 2

Like surds only.

If needed simplify surds first

Question 3

Multiplying and dividing

Answer 3

Root a x root b =root ab

Root a/b = root a / root b

Question 4

Expanding brackets with surds

Answer 4

Same as normal expanding

Root2(6 +root3) = 6root2 + root6

Question 5

Rationalising the denominator

Answer 5

Multiply by the surf denominator

2/root3 = 2/root3 x root3/ root3
= 2root3 / 3

Question 6

Rationalising the denominator using conjugate surds

Answer 6

4/1+root2 x 1-root2/1-root2

= 4(1-root2)
——————
(1+root2)(1-root2)

= 4-4root2
———
1 -2

= 4 -4root2

     - 1

= -(4 - 4root2)
= -4 + 4root2