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How do you find the simplest radical form of 433?

Last updated date: 29th Feb 2024
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IVSAT 2024
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Hint: The radical form of any number means the square root of that number. We further simplify the terms inside the square root to evaluate the simplest radical form of the number. Thus, we shall find the square root of 433 but since 433 is a prime number therefore, its square root will not be further simplified in radical form. However, we can express it in decimals.

Complete step-by-step answer:
We have a number 433. It is expressed as $\sqrt{433}$ in its radical form.
In order to simplify this term further, we shall find the factors of 433.
On calculating the factors, we find that 433 has only two factors which is 1 and the number itself, 433. This is because 433 is a prime number.
However, the square root of 433 rounded off to the nearest two decimal places is $20.81$.
Therefore, the simplest radical form of 433 is $\sqrt{433}$.

The radical form of any number is equal to its square root. In the process of finding the square root of a number, we find the factors of that number and then group the like factors together. If any factor occurs twice or occurs 2k times (where k is a constant written to express the term as multiples of 2), then we make pairs of that factor and take it outside the square root. The factor of the number which had occurred only once is left behind under the square root sign only.