4. Addition and Subtraction of Radicals

In algebra, we can combine terms that are similar eg.

2a + 3a = 5a

8x2 + 2x − 3x2 = 5x2 + 2x

Similarly for surds, we can combine those that are similar. They must have the same radicand (number under the radical) and the same index (the root that we are taking).

 

Example 1

(a) math expression

Answer:

math expression

We can do this because the radicand is 7 in each case and the index is 1/2 (that is, we are taking square root) in each case.

(b) math expression

Answer:

math expression

(c) math expression

Answer:

math expression


Example 2

(a) math expression

Answer:

In each part, we are taking square root, but the number under the square root is different. We need to simplify the radicals first and see if we can combine them.

math expression

(b) math expression

Answer:

math expression

 

Example 3

Simplify:

math expression

Answer:

Our aim here is to remove the radicals from the denominator of each fraction and then to combine the terms into one expression.

math expression

We multiply top and bottom of each fraction with their denominators. This gives us a perfect square in the denominator in eachcase, and we can remove the radical.

We then simplify and see that we have like terms (√6a).

We then proceed to subtract the fractions by finding a common denominator (3a).

 

Exercises

Q1 math expression


Answer

Q2 math expression


Answer

Q3 math expression


Answer



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