Questions: Express in simplest radical form. 6 sqrt(175) + 7 sqrt(28)

Express in simplest radical form. 6 sqrt(175) + 7 sqrt(28)
Transcript text: Express in simplest radical form. \[ 6 \sqrt{175}+7 \sqrt{28} \]
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Solution

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Solution Steps

Step 1: Simplify Each Radical

We start by simplifying the radicals in the expression \( 6 \sqrt{175} + 7 \sqrt{28} \).

For \( \sqrt{175} \): \[ \sqrt{175} = \sqrt{25 \cdot 7} = \sqrt{25} \cdot \sqrt{7} = 5\sqrt{7} \] Thus, \( 6 \sqrt{175} = 6 \cdot 5 \sqrt{7} = 30 \sqrt{7} \).

For \( \sqrt{28} \): \[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \] Thus, \( 7 \sqrt{28} = 7 \cdot 2 \sqrt{7} = 14 \sqrt{7} \).

Step 2: Combine Like Terms

Now we combine the simplified terms: \[ 30 \sqrt{7} + 14 \sqrt{7} = (30 + 14) \sqrt{7} = 44 \sqrt{7} \]

Step 3: Final Expression

The expression \( 6 \sqrt{175} + 7 \sqrt{28} \) simplifies to: \[ 44 \sqrt{7} \]

Final Answer

\(\boxed{44 \sqrt{7}}\)

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