Simplifying radical expressions7/29/2023 Well, sometimes, instead of approximating the result, it's better to transform it a little. The 25 was easy, but what is, say, √288? On the one hand, we have 16² = 256, and on the other, 17² = 289, so √288 should be somewhere between 16 and 17. Let us focus on such expressions for the remainder of this section, so for now, you can consider our tool as a simplify square roots calculator. For instance, we know that 5² = 25, so the square root of 25 is √25 = 5. That means that they are the inverse operation to taking the second power (i.e., the square) of a number. Nevertheless, there are some nifty tricks that we can use, and you bet we will show you all of them! Let's first see how to simplify square roots. Well, most probably, we use some external tools for more complicated tasks – something like our simplify radical expressions calculator. How do we see that the result is 5 from such a big and complicated number? Or what do we do if it's 390,624 instead? What could that monstrosity be? After all, sometimes the number we get is not written as 5 8 but rather as 390,625. Of course, taking the root is not always that simple. We're aware that radicals of odd order also apply to negative numbers and that rational numbers have roots as well, but, for simplicity, we limit ourselves to the non-negative integer case. The number under the root must be a non-negative integer.The order of a radical must be an integer greater or equal to 2.Let us take this opportunity to mention a couple of essential rules that govern Omni's simplify radicals calculator. In other words, while the exponent turns 5 into 5 8, the (eighth) root makes 5 8 into 5. Taking the root (also called radical) is the inverse operation to the above. The small number in the superscript tells us how many times we multiply the big number – in this case, we have eight fives. Whenever we multiply by the same number several times, we can save ourselves some time (time is money, after all), and instead of repeating the multiplication, write the whole thing using exponents.
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