Problem: Article: The goal of simplifying a square root is to rewrite it in a form that is easy to understand and to use in math problems. Factoring breaks down a large number into two or more smaller factors, for instance turning 9 into 3 x 3. Once we find these factors, we can rewrite the square root in simpler form, sometimes even turning it into a normal integer. For example, √9 = √(3x3) = 3. Follow the steps below to learn this process for more complicated square roots. If the number under the square root is even, divide it by 2. If your number is odd, try dividing it by 3 instead. If neither of these gives you a whole number, move down this list, testing the other primes until you get a whole number result. You only need to test the prime numbers, since all other numbers have prime numbers as their factors. For example, you don't need to test 4, because any number divisible by 4 is also divisible by 2, which you already tried.  2 3 5 7 11 13 17 Keep everything underneath the square root sign, and don't forget to include both factors. For example, if you're trying to simplify √98, follow the step above to discover that 98 ÷ 2 = 49, so 98 = 2 x 49. Rewrite the "98" in the original square root using this information: √98 = √(2 x 49). Before we can simplify the square root, we keep factoring it until we've broken it down into two identical parts. This makes sense if you think about what a square root means: the term √(2 x 2) means "the number you can multiply with itself to equal 2 x 2." Obviously, this number is 2! With this goal in mind, let's repeat the steps above for our example problem, √(2 x 49):  2 is already factored as low as it will go. (In other words, it's one of those prime numbers on the list above.) We'll ignore this for now and try to divide 49 instead. 49 can't be evenly divided by 2, or by 3, or by 5. You can test this yourself using a calculator or long division. Because these don't give us nice, whole number results, we'll ignore them and keep trying. 49 can be evenly divided by seven. 49 ÷ 7 = 7, so 49 = 7 x 7. Rewrite the problem: √(2 x 49) = √(2 x 7 x 7). Once you've broken the problem down into two identical factors, you can turn that into a regular integer outside the square root. Leave all other factors inside the square root. For example, √(2 x 7 x 7) = √(2)√(7 x 7) = √(2) x 7 = 7√(2). Even if it's possible to keep factoring, you don't need to once you've found two identical factors. For example, √(16) = √(4 x 4) = 4. If we kept on factoring, we'd end up with the same answer but have to do more work: √(16) = √(4 x 4) = √(2 x 2 x 2 x 2) = √(2 x 2)√(2 x 2) = 2 x 2 = 4. With some large square roots, you can simplify more than once. If this happens, multiply the integers together to get your final problem. Here's an example:  √180 = √(2 x 90) √180 = √(2 x 2 x 45) √180 = 2√45, but this can still be simplified further. √180 = 2√(3 x 15) √180 = 2√(3 x 3 x 5) √180 = (2)(3√5) √180 = 6√5 Some square roots are already in simplest form. If you keep factoring until every term under the square root is a prime number (listed in one of the steps above), and no two are the same, then there's nothing you can do. You might have been given a trick question! For example, let's try to simplify √70:  70 = 35 x 2, so √70 = √(35 x 2) 35 = 7 x 5, so √(35 x 2) = √(7 x 5 x 2) All three of these numbers are prime, so they cannot be factored further. They're all different, so there's no way to "pull out" an integer. √70 cannot be simplified.
Summary: Understand factoring. Divide by the smallest prime number possible. Rewrite the square root as a multiplication problem. Repeat with one of the remaining numbers. Finish simplifying by "pulling out" an integer. Multiply integers together if there are more than one. Write "cannot be simplified" if there are no two identical factors.

In one sentence, describe what the following article is about: Sites are added to the Google Search index automatically as Google's bots scour the web for new content. You don't need to actively do anything to submit your site to Google, but there are several things you can do to increase your chances of being indexed. The organization and hierarchy of your website has a big impact on whether or not your content will be indexed by Google. This means that your pages should have a manageable number of links, that all of your content is easily reachable with single links, If you have well-written, helpful content on your site, you have a higher chance of being indexed by Google. Avoid copying and pasting content from other sites, and make sure all of your content is clear, concise, and relates to your site's purpose. Include words and phrases that readers would use to find your site. Make sure that important words and names are written out in text, and not just shown in pictures. Google cannot index words that are embedded in pictures. A sitemap is a file that contains the layout of your site. This allows the Google bots to quickly see all of your site's pages, allowing it to index much more effectively. Click here for instructions on creating a sitemap from scratch or by using a tool. This file controls what can and cannot be seen by the Google bots. The robots.txt file is used to tell these bots which parts of your webpage should not be indexed, and which parts are open for indexing. If your robots.txt file isn't properly formatted, Google bots may be skipping your webpage entirely. Click here for instructions on properly creating a robots.txt file. You can manually submit your site to be indexed by Google. This does not guarantee that you will be indexed, and there is no timeline given for how soon it may happen. To add your site to the index queue, visit google.com/addurl and paste your site's URL into the field. This is not required to get your site indexed. As long as you meet the guidelines outlined above, your site should be indexed automatically at some point. This is a utility for webmasters that allows you to better control how your site appears in Google Search results. You can log into the console at google.com/webmasters. Click the "Add A Property" button and paste your website's URL into the field. You will be prompted to verify that you own the website. Follow the prompts to verify that you own the domain that you've added. You can do this through your domain name provider, or you can upload a special file to your site's server to prove that you have access. After adding your site, Search Console will provide you with several suggestions for increasing your site's visibility. Scroll through the list and complete each suggested step.  You'll be asked to include all versions of your site, including "www." versions and non-"www." versions. You can choose your preferred target country. You'll be asked to submit the sitemap that you created earlier. As your site starts getting search traffic, you can use Search Console to see detailed reports and problem areas. You can see where the crawlers have had issues, test your robots.txt file, update your sitemaps, and more.
Summary:
Understand the process. Design your site with a clear organization. Make sure your content is original and helpful. Create a sitemap. Ensure that your robots.txt file is properly written. Submit your site to Google. Log into the Google Search Console. Add your site to the Search Console. Verify your ownership. Fill out the requested information. Use Search Console to manage your site's search presence.