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How do you find the square root of 2000 in radical form?

Answer
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Hint: In this problem, we have to simplify 2000 in radical form. We can write in whole square form inside the square root, then we can convert the square root, that is radical form, to the fractional exponent. We can then cancel the power of the terms and the fractional exponent raised to get the simplified form. We can use the formula an=a1n to convert the radical to fractional exponent.

Complete step-by-step solution:
We know that the given expression to be simplified is 2000.
We can write the terms inside the square root in whole square form, as we can write as
2000=400×5=(20)2×5 …… (1)
Now we can convert the square root form, that is the radical form, into fractional exponent form.
The formula to convert the radical form to fractional exponent form is an=a1n.
Now we can apply the above formula in the expression (1), we get
20002=(20)2×12×5
Now we can cancel the similar numbers in the power, we get
205
Therefore, the simplified form of 2000 is 205.

Note: Students make mistakes while writing the whole square form inside the square root, it is possible only when the given numbers are perfect squares. If the given numbers are perfect squares, we can solve it in a simple way, if it is not a perfect square, then we can use another method to solve those problems. We should remember that, to solve these types of problems, we should know how to convert the radicals to fractional exponents.
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