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Let’s check out your problem:
Simplify.
\newline
6
27
6 \sqrt{27}
6
27
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Math Problems
Algebra 1
Simplify radical expressions: mixed review
Full solution
Q.
Simplify.
\newline
6
27
6 \sqrt{27}
6
27
Break down into prime factors:
First, let's break down
27
27
27
into its prime factors.
\newline
27
=
3
×
3
×
3
27 = 3 \times 3 \times 3
27
=
3
×
3
×
3
Rewrite using prime factors:
Now, we rewrite the square root of
27
27
27
using its prime factors.
6
27
=
6
×
3
×
3
×
3
6\sqrt{27} = 6 \times \sqrt{3 \times 3 \times 3}
6
27
=
6
×
3
×
3
×
3
Group identical factors:
Next, we group the identical factors under the square root.
\newline
6
×
3
×
3
×
3
=
6
×
3
2
×
3
6 \times \sqrt{3 \times 3 \times 3} = 6 \times \sqrt{3^2 \times 3}
6
×
3
×
3
×
3
=
6
×
3
2
×
3
Take out of square root:
We know that
3
2
\sqrt{3^2}
3
2
is just
3
3
3
, so we can take it out of the square root.
6
×
3
2
×
3
=
6
×
3
×
3
6 \times \sqrt{3^2 \times 3} = 6 \times 3 \times \sqrt{3}
6
×
3
2
×
3
=
6
×
3
×
3
Multiply outside numbers:
Now, we multiply the numbers outside the square root.
6
×
3
×
3
=
18
3
6 \times 3 \times \sqrt{3} = 18\sqrt{3}
6
×
3
×
3
=
18
3
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