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Let’s check out your problem:
Simplify.
\newline
175
\sqrt{175}
175
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Math Problems
Algebra 1
Simplify radical expressions: mixed review
Full solution
Q.
Simplify.
\newline
175
\sqrt{175}
175
Breakdown Prime Factors:
Let's break down
175
175
175
into its prime factors.
\newline
Prime factorization of
175
175
175
is
5
×
5
×
7
5 \times 5 \times 7
5
×
5
×
7
.
\newline
175
=
5
×
5
×
7
\sqrt{175} = \sqrt{5 \times 5 \times 7}
175
=
5
×
5
×
7
Group Identical Factors:
Now, group the identical factors.
175
=
5
2
×
7
\sqrt{175} = \sqrt{5^2 \times 7}
175
=
5
2
×
7
Separate Square:
Use the product property of radicals to separate the square.
175
=
5
2
×
7
\sqrt{175} = \sqrt{5^2} \times \sqrt{7}
175
=
5
2
×
7
Final Result:
Square root of
5
2
5^2
5
2
is
5
5
5
, so we have:
\newline
175
=
5
×
7
\sqrt{175} = 5 \times \sqrt{7}
175
=
5
×
7
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