Article: An easy way to factor a number is by creating a factor tree diagram. Read Do a Factor Tree for complete instructions.  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, 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. Keep all the factors under the radical sign. 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}}.} Since you are finding a square root, by pairing up like factors, you can easily simplify the expression. 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. The square root of any pair of factors will equal the factor, because x×x=x2{\displaystyle x\times x=x^{2}} and x2=x{\displaystyle {\sqrt {x^{2}}}=x}. Place this number in front of the radical sign. If the expression already has a coefficient, multiply the two numbers.  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}}}. This will make the adding process much easier. 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}}}
Question: What is a summary of what this article is about?
Factor each radicand into prime numbers. Rewrite the expression. Circle pairs of like factors under each radical. Factor out coefficients by identifying paired factors under each radical. Rewrite your problem, using the simplified terms.
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Question: What is a summary of what this article is about?
Use your hands. Care for animals. Use your people skills. Advance with Technology. Draw on your artistic talents. Write as a freelancer. Post on social media.