{"id":12435,"date":"2020-07-03T21:30:57","date_gmt":"2020-07-03T13:30:57","guid":{"rendered":"https:\/\/www.intmath.com\/blog\/?p=12435"},"modified":"2020-07-03T21:30:57","modified_gmt":"2020-07-03T13:30:57","slug":"simplifying-radical-expressions","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/simplifying-radical-expressions-12435","title":{"rendered":"Simplifying Radical Expressions"},"content":{"rendered":"

Before we begin simplifying radical expressions, let\u2019s recall the properties of them. Take a look at the expression below:<\/p>\n

\"\"\"\"\u200b<\/p>\n

Looking at the radical expression above, we can determine that\u00a0X\u00a0<\/em>is the\u00a0radicand<\/em>\u00a0<\/strong>of the expression. Meanwhile, \u221a\u00a0is the\u00a0radical symbol\u00a0<\/strong>while\u00a0n<\/em>\u00a0is the\u00a0index<\/strong>. In this case, should you encounter a radical expression that is written like this:\"\"\"\"\u200b<\/p>\n

\"\"\"\"\u200b<\/p>\n

You can easily tell that the radicand of the expression equals to 25 while the index equals to 2. Radical expressions with the index of 2 are also referred to as square root. Since that is the case, we can hide the index part so it would be written like this:<\/p>\n

\"\"\"\"\u200b<\/p>\n

Basics of Simplifying Expressions<\/h2>\n

If we want to simplify the expression above, we can do it like so:<\/p>\n

\"\"\"\"\u200b<\/p>\n

Simplifying an expression meaning we are replacing it with an equivalent that is easier to digest and, if possible, shorter. In the example above, the simplification of\u00a0\"\"\"\"\u200b\u00a0is 5. If we want to simplify other radicals such as\u00a0\"\"\"\"\u200b\"\"\"\"\u200b, and\u00a0\"\"\"\"\u200b\u00a0that has\u00a0perfect square<\/em>\u00a0radicands\u201425 is also a perfect square, then the result would be 6, 7, and 4 respectively.<\/p>\n

Recall that perfect squares are radicands that have an integer as its square root (e.g. 5, an integer, is the square root of 25). In that case, what if we want to simplify other radicals that don\u2019t have a perfect square as its radicands?<\/p>\n

Simplifying Radicals Expressions with Imperfect Square Radicands<\/h2>\n

Imperfect squares are the opposite of perfect squares. As radicands, imperfect squares don\u2019t have an integer as its square root. Instead, the square root would be a number which decimal part would continue on endlessly without end and won\u2019t show any repeating pattern. Here are some examples:<\/p>\n