Problem: Write an article based on this summary: 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.

Answer: 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}}}


Problem: Write an article based on this summary: Play the game for 7 to 10 hours. Take notes on what you appreciate about the game. Write down what could be improved about the game. Note how the game compares to other games like it.

Answer: Many video games can take upwards of 100 hours to complete. However, most publications expect a review within 1 week of the game being released. Try to play the video game that you are reviewing for at least 7 hours to get a feel for it. Explore as much of the game as you can in this timeframe. If the game has different levels, try to level up as many times as possible. If the game is an open world, explore as much of it as you can. Your notes will translate directly into what you put in your review. Use a computer or a notebook to write down what you like about the game. Pay attention to playability, sound, graphics, and in-game purchases. Jot down anything that sticks out to you, even if it is small. Details as small as the trees waving in the wind or a character’s headband can help a reader envision the in-game world when they read your review. Not every game is perfect, and your review should focus on the improvements that you think could be made as well as the positives. Take note of what you didn’t love about the game. Maybe the graphics are clunky, or the load times are too long. If anything annoys you even slightly, be sure to write it down. You’ve probably played a lot of video games that could be comparable to the one you are reviewing. Think about games that are in the same genre as the one you are playing. Is it an action-based game? A horror game? A racing one? Then, think about which ones you liked better or worse. Would you play this one more or less than other games? For example, you could say, “This racing game has more car model options, but less customizable pieces than their last release.”


Problem: Write an article based on this summary: Choose your form of gum. Find the perfect flavor. Decide if you want regular or sugar-free gum.

Answer:
Do you want a stick of gum, a tab of gum, or even a gumball? Different brands come in different shapes and sizes, and you can experiment to find out which one you prefer. Brands like Extra and Wrigley market their gum in sticks, while Orbit, Trident, and Eclipse come in smaller tabs or mini-sticks. Double Bubble makes candy gum balls, and Big League Chew sells their gum shredded in a pouch. There is a kind of chewing gum for everyone! Does your breath need freshening? If so, you should look for a minty flavor that will leave your mouth feeling sparkling clean. Try something like spearmint or peppermint and you'll feel like you just brushed. If you want something with more of a fruity kick, there are flavors like berry and watermelon that will do the trick. People looking to satisfy a sweet tooth should check out the Extra Dessert Delights- those flavors include treats like rainbow sherbet, mint chocolate chip, and strawberry shortcake! Regular gum contains sugar, which can lead to increased tooth decay.Sugar-free gum uses chemical sweeteners, such as aspartame.. There is a caloric difference of about 5 calories between the two types. If you're opting for sugar-free gum, look for gum with a seal from the American Dental Association. The ADA Seal on a package of gum means that gum has been proven to be healthy and safe.