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Let’s check out your problem:
Multiply. Write your answer in simplest form.
\newline
3
(
−
2
−
5
)
\sqrt{3}(-2 - \sqrt{5})
3
(
−
2
−
5
)
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Math Problems
Algebra 1
Simplify radical expressions using the distributive property
Full solution
Q.
Multiply. Write your answer in simplest form.
\newline
3
(
−
2
−
5
)
\sqrt{3}(-2 - \sqrt{5})
3
(
−
2
−
5
)
Distribute
3
\sqrt{3}
3
:
We need to distribute
3
\sqrt{3}
3
across the terms inside the parentheses.
3
(
−
2
−
5
)
=
3
×
−
2
+
3
×
−
5
\sqrt{3}(-2 - \sqrt{5}) = \sqrt{3} \times -2 + \sqrt{3} \times -\sqrt{5}
3
(
−
2
−
5
)
=
3
×
−
2
+
3
×
−
5
Multiply by
−
2
-2
−
2
:
Now we multiply
3
\sqrt{3}
3
by
−
2
-2
−
2
.
\newline
3
×
−
2
=
−
2
3
\sqrt{3} \times -2 = -2\sqrt{3}
3
×
−
2
=
−
2
3
Multiply by
−
5
-\sqrt{5}
−
5
:
Next, we multiply
3
\sqrt{3}
3
by
−
5
-\sqrt{5}
−
5
.
\newline
3
×
−
5
=
−
3
×
5
=
−
15
\sqrt{3} \times -\sqrt{5} = -\sqrt{3 \times 5} = -\sqrt{15}
3
×
−
5
=
−
3
×
5
=
−
15
Combine to get final answer:
Combine the two products to get the final answer.
\newline
−
2
3
−
15
-2\sqrt{3} - \sqrt{15}
−
2
3
−
15
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