Add and Subtract Radical Expressions Questions with Solutions
Grade 10 questions on how to add and subtract expressions with radicals and their solutions are presented.
DefinitionRadical expressions are like if they have the same index and the same radicand.
Examples



Add and Subtract Like Radicals
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.

More Examples
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



Questions With Solutions
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.


More Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
More Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
Home Page