23 lines
2.1 KiB
Markdown
23 lines
2.1 KiB
Markdown
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---
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title: Adding and Subtracting Radicals and Square Roots
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---
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## Adding and Subtracting Radicals and Square Roots
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You can add "like" square roots in the same way that you add other kinds of numbers. "Like" square roots are terms that have the same radical parts.
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<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/article1img1.png?raw=true" alt="Formula showing 2 times the square root of 3 plus 2 times the square root of 3 with arrows pointing to the square root parts as the radical parts">
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The terms above can be simplified as follows:
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<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/article1img2.png?raw=true" alt="Formula showing 2 times the square root of 3 plus 2 times the square root of 3 equals (2 + 2) times the square root of 3 which equals 4 times the square root of 3">
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Expressions with unlike radicals can be simplified in some cases. Notice that the principal roots of 100 and 9 are square numbers.
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<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/article1img3.png?raw=true" alt="Formula showing the square root of 100 plus the square root of 9 equals 10 plus 3 which equals 13">
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<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/article1img4.png?raw=true" alt="Formula showing 4 times the square root of 100 plus 3 times the square root of 9 equals 4 times 10 plus 3 times 3 which equals 49">
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Remember that without like terms there is a limit to how much you can simplify.
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<img src="https://github.com/codersc/freeCodeCamp-article-images/blob/master/article1img5.png?raw=true" alt="Formula showing 2 times the square root of 2 plus 2 times the square root of 2 plus the square root of 3 equals 4 times the square root of 2 plus the square root of 3">
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<img src="http://www.sciweavers.org/tex2img.php?eq=%20%5Csqrt%7B12%7D%20%2B%20%5Csqrt%7B3%7D%20%3D%20%5Csqrt%7B4%20%5Ctimes%203%7D%20%2B%20%5Csqrt%7B3%7D&bc=White&fc=Black&im=jpg&fs=12&ff=arev&edit=0" align="center" border="0" alt=" \sqrt{12} + \sqrt{3} = \sqrt{4 \times 3} + \sqrt{3}" width="214" height="26" />
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