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Let’s check out your problem:
Multiply. Write your answer in simplest form.
\newline
2
(
7
+
5
)
\sqrt{2}(7 + \sqrt{5})
2
(
7
+
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
2
(
7
+
5
)
\sqrt{2}(7 + \sqrt{5})
2
(
7
+
5
)
Distribute
2
\sqrt{2}
2
:
We need to distribute
2
\sqrt{2}
2
across the terms inside the parentheses.
2
(
7
+
5
)
=
2
×
7
+
2
×
5
\sqrt{2}(7 + \sqrt{5}) = \sqrt{2} \times 7 + \sqrt{2} \times \sqrt{5}
2
(
7
+
5
)
=
2
×
7
+
2
×
5
Multiply by
7
7
7
:
Now we multiply
2
\sqrt{2}
2
by
7
7
7
.
2
×
7
=
7
2
\sqrt{2} \times 7 = 7\sqrt{2}
2
×
7
=
7
2
Multiply by
5
\sqrt{5}
5
:
Next, we multiply
2
\sqrt{2}
2
by
5
\sqrt{5}
5
.
2
×
5
=
2
×
5
=
10
\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} = \sqrt{10}
2
×
5
=
2
×
5
=
10
Combine products:
Combine the two products to get the final expression in simplest form.
7
2
+
10
7\sqrt{2} + \sqrt{10}
7
2
+
10
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