Grade 10 questions on how to add and subtract expressions with radicals and their solutions are presented.
Radical expressions are like if they have the same index and the same radicand.
Examples
are like radicals because they have the same index (root number which is 3) and the same radicand (number under the radical which is 5.
are not like radicals because they have different radicands 8 and 9.
are like radicals because they have the same index (2 for square root) and the same radicand 2 x.
Only like radicals may be added or subtracted.
Examples
Simplify the following expressions
Solutions to the Above Examples
The above expressions are simplified by first factoring out the like radicals and then adding/subtracting.
Simplify the following expressions
The above expressions are simplified by first transforming the unlike radicals to like radicals and then adding/subtracting
When it is not obvious to obtain a common radicand from 2 different radicands, decompose them into prime numbers. Decompose 12 and 108 into prime factors as follows.
We now substitute 12 and 108 by their prime factors and simplify
Simplify the following expressions
3. The 3 radicands in the given expression -√ 32 - 2√ 50 + 3√ 200 are different but note that 32, 50 and 200 may be written as 2 times a number that is a perfect square as follows: 32=2 * 16, 50=2 * 25 and 100=2 * 100. Substitute in the given expression and simplify.
Decompose 28 and 63 into prime factors as follows: 28=2 2 * 7 , 63=3 2 * 7 and substitute into the given expression and simplify
7. 
