{"id":97495,"date":"2021-10-13T16:13:31","date_gmt":"2021-10-13T21:13:31","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=97495"},"modified":"2026-05-21T12:56:01","modified_gmt":"2026-05-21T17:56:01","slug":"simplifying-square-roots","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/simplifying-square-roots\/","title":{"rendered":"Simplifying Square Roots Overview"},"content":{"rendered":"

The square root of a number is a number that, when multiplied by itself, results in the original number. For example, \\(5\\times5=25\\), therefore, the square root of \\(25\\) is \\(5\\). The radical symbol, \\(\\sqrt{ }\\), is used to represent square roots. The two statements, \u201cWhat is the square root of \\(36\\)?\u201d and \u201cWhat is \\(\\sqrt{36}\\)?\u201d are read the exact same way.<\/p>\n

Simplifying Square Root Sample Questions<\/a><\/div>\n

To simplify a square root, we simply find the value that when multiplied by itself gives us the original number. When a number\u2019s square root is a whole number, the original number is called a perfect square.<\/p>\n

Here are some examples of perfect squares:<\/p>\n\\(\\sqrt{4}=2\\)\n\\(\\sqrt{9}=3\\)\n\\(\\sqrt{16}=4\\)\n\\(\\sqrt{25}=5\\)\n

When a square root does not simplify to a whole number, we simplify what we can and whatever is remaining stays under the radical symbol. For example, to simplify \\(\\sqrt{28}\\), we will look at the factors of \\(\\sqrt{28}\\) to see if there are any perfect squares. \\(28=2\\times2\\times7\\) or \\(4\\times7\\). Since \\(4\\) is a perfect square and \\(\\sqrt{4}=2\\), we can pull that out and we are left with \\(7\\) under the radical, so \\(\\sqrt{28}=2\\sqrt{7}\\).<\/p>\n

Example<\/h3>\n

Simplify \\(\\sqrt{180}\\).<\/p>\n

<\/div>\n\\(180=2\\times2\\times3\\times3\\times5\\)\n

Therefore, \\(\\sqrt{180}=2\\times3\\sqrt{5}=6\\sqrt{5}\\).<\/p>\n\"Click<\/a>\n

Simplifying Square Root Sample Questions<\/h2>\n

Here are a few sample questions going over simplifying square roots.
\n\n\t\t\t\t

\n\t\t\t\t\tQuestion #1:<\/strong>\n\t\t\t\t\t

 
\nWrite \\(\\sqrt{175}\\) in the most simplified form possible.<\/p>\n<\/div>\n\t\t\t\t\t

\\(5\\sqrt{7}\\)<\/div>
\\(7\\sqrt{5}\\)<\/div>
\\(25\\sqrt{7}\\)<\/div>
\\(35\\sqrt{5}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t
\n\t\t\t\t\t\tAnswer:<\/strong>

To simplify the expression \\(\\sqrt{175}\\), we will start by finding the factors of \\(175\\), which is \\(5\\times5\\times7\\). Since \\(5\\times5\\) is a perfect square, we can take one \\(5\\) out and we are left with \\(7\\) under the radical; therefore, \\(\\sqrt{175}=5\\sqrt{7}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t

\n\t\t\t\t\tQuestion #2:<\/strong>\n\t\t\t\t\t

 
\nWhich shows \\(\\sqrt{208}\\) in its most simplified form? <\/p>\n<\/div>\n\t\t\t\t\t

\\(2\\sqrt{52}\\)<\/div>
\\(4\\sqrt{52}\\)<\/div>
\\(4\\sqrt{13}\\)<\/div>
\\(13\\sqrt{4}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t