Express 20^1/2 in simplest radical form.

1 answer

To express \( 20^{1/2} \) in simplest radical form, we first recognize that \( 20^{1/2} \) is equivalent to the square root of 20:

\[ 20^{1/2} = \sqrt{20} \]

Next, we simplify \( \sqrt{20} \) by factoring 20 into its prime factors. The number 20 can be factored as follows:

\[ 20 = 4 \times 5 = 2^2 \times 5 \]

Now we can express the square root of 20 using its factors:

\[ \sqrt{20} = \sqrt{4 \times 5} \]

We can use the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \):

\[ \sqrt{20} = \sqrt{4} \times \sqrt{5} \]

Since \( \sqrt{4} = 2 \), we have:

\[ \sqrt{20} = 2 \times \sqrt{5} \]

Thus, the simplest radical form of \( 20^{1/2} \) is:

\[ \boxed{2\sqrt{5}} \]