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Let’s check out your problem:
Simplify.
\newline
2
125
2 \sqrt{125}
2
125
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Math Problems
Algebra 1
Simplify radical expressions: mixed review
Full solution
Q.
Simplify.
\newline
2
125
2 \sqrt{125}
2
125
Breakdown into Prime Factors:
First, let's break down
125
125
125
into its prime factors.
\newline
125
=
5
×
5
×
5
125 = 5 \times 5 \times 5
125
=
5
×
5
×
5
Rewrite Using Prime Factors:
Now, we can rewrite the square root of
125
125
125
using its prime factors.
2
125
=
2
5
×
5
×
5
2\sqrt{125} = 2\sqrt{5 \times 5 \times 5}
2
125
=
2
5
×
5
×
5
Pair Like Factors:
We can pair the like factors under the square root.
2
5
×
5
×
5
=
2
5
2
×
5
2\sqrt{5 \times 5 \times 5} = 2\sqrt{5^2 \times 5}
2
5
×
5
×
5
=
2
5
2
×
5
Take Square Root:
Next, we can take the square root of the perfect square, which is
5
2
5^2
5
2
.
\newline
2
5
2
×
5
=
2
×
5
×
5
2\sqrt{5^2 \times 5} = 2 \times 5 \times \sqrt{5}
2
5
2
×
5
=
2
×
5
×
5
Multiply Outside Numbers:
Finally, we multiply the numbers outside the square root.
2
×
5
×
5
=
10
5
2 \times 5 \times \sqrt{5} = 10\sqrt{5}
2
×
5
×
5
=
10
5
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