A radicand is the number under the radical sign. A prime number is a number that can only be divided evenly by 1 and itself,[2] X Research source for example, 2, 3, 5, 7, 11, etc. You do NOT need to factor any coefficients. A coefficient is a number in front of the radical sign. Let’s say, for example, that you want to add 20+445+5+7. {\displaystyle {\sqrt {20}}+4{\sqrt {45}}+{\sqrt {5}}+{\sqrt {7}}. }To do this, you need to factor 20{\displaystyle 20} as 2×2×5{\displaystyle 2\times 2\times 5}. You also need to factor 45{\displaystyle 45} as 3×3×5{\displaystyle 3\times 3\times 5}. If a radicand is already a prime number, it does not need to be factored. For example, since 5{\displaystyle 5} and 7{\displaystyle 7} are already prime numbers, 5{\displaystyle {\sqrt {5}}} and 7{\displaystyle {\sqrt {7}}} do not need to be factored.
For example, after factoring the radicands, the example expression would be2×2×5+43×3×5+5+7. {\displaystyle {\sqrt {2\times 2\times 5}}+4{\sqrt {3\times 3\times 5}}+{\sqrt {5}}+{\sqrt {7}}. }
For example, 2×2×5{\displaystyle {\sqrt {2\times 2\times 5}}} has a pair of 2s, so draw a circle around them. 43×3×5{\displaystyle 4{\sqrt {3\times 3\times 5}}} has a pair of 3s, so draw a circle around them.
For example:2×2×5{\displaystyle {\sqrt {2\times 2\times 5}}}=45{\displaystyle ={\sqrt {4}}{\sqrt {5}}}=25{\displaystyle =2{\sqrt {5}}}So, 20{\displaystyle {\sqrt {20}}} simplifies to 25{\displaystyle 2{\sqrt {5}}}. 43×3×5{\displaystyle 4{\sqrt {3\times 3\times 5}}}=4×95{\displaystyle =4\times {\sqrt {9}}{\sqrt {5}}}=(4×3)5{\displaystyle =(4\times 3){\sqrt {5}}}=125{\displaystyle =12{\sqrt {5}}}So, 445{\displaystyle 4{\sqrt {45}}}simplifies to 125{\displaystyle 12{\sqrt {5}}}.
For example:20+445+5+7{\displaystyle {\sqrt {20}}+4{\sqrt {45}}+{\sqrt {5}}+{\sqrt {7}}} simplifies to25+125+5+7{\displaystyle 2{\sqrt {5}}+12{\sqrt {5}}+{\sqrt {5}}+{\sqrt {7}}}
A coefficient is the number in front of the radical sign. For example, write 5{\displaystyle {\sqrt {5}}} as 15{\displaystyle 1{\sqrt {5}}}.
The radicand is the number underneath the radical sign. For example, you can add the first three terms in the expression 25+125+5+7{\displaystyle 2{\sqrt {5}}+12{\sqrt {5}}+{\sqrt {5}}+{\sqrt {7}}}, because they all have the same radicand (5).
For example, 25+125+15=155{\displaystyle 2{\sqrt {5}}+12{\sqrt {5}}+1{\sqrt {5}}=15{\sqrt {5}}}.
For example, 155+7{\displaystyle 15{\sqrt {5}}+{\sqrt {7}}}.
