Question
find the square root of 250 in radicals
Answers
GPT-4o mini
To find the square root of 250 in radical form, we first factor 250 into its prime factors:
\( 250 = 25 \times 10 = 25 \times (5 \times 2) = 5^2 \times 5 \times 2 = 5^3 \times 2 \).
Now, we can take the square root:
\[
\sqrt{250} = \sqrt{5^3 \times 2} = \sqrt{5^2 \times 5 \times 2}.
\]
Using the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):
\[
\sqrt{250} = \sqrt{5^2} \times \sqrt{5} \times \sqrt{2} = 5\sqrt{10}.
\]
So, the square root of 250 in radical form is:
\[
\sqrt{250} = 5\sqrt{10}.
\]
\( 250 = 25 \times 10 = 25 \times (5 \times 2) = 5^2 \times 5 \times 2 = 5^3 \times 2 \).
Now, we can take the square root:
\[
\sqrt{250} = \sqrt{5^3 \times 2} = \sqrt{5^2 \times 5 \times 2}.
\]
Using the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):
\[
\sqrt{250} = \sqrt{5^2} \times \sqrt{5} \times \sqrt{2} = 5\sqrt{10}.
\]
So, the square root of 250 in radical form is:
\[
\sqrt{250} = 5\sqrt{10}.
\]