To simplify the expression \( \sqrt{5} + 3\sqrt{45} \), let's first simplify \( 3\sqrt{45} \).
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We can factor \( 45 \) as \( 9 \times 5 \), and since \( \sqrt{9} = 3 \): \[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \]
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Now, substituting this back into the expression gives: \[ 3\sqrt{45} = 3(3\sqrt{5}) = 9\sqrt{5} \]
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Therefore, we can combine \( \sqrt{5} + 9\sqrt{5} \): \[ \sqrt{5} + 9\sqrt{5} = 10\sqrt{5} \]
Now, the original expression \( \sqrt{5} + 3\sqrt{45} \) simplifies to \( 10\sqrt{5} \).
So we can complete the statement:
\[ 10 \sqrt{5} + 3\sqrt{45} = 13\sqrt{5} \]
Thus, the completed expression is:
\[ 10 \sqrt{5} + 3 \sqrt{45} = 10 \sqrt{5} \]
The blanks can be filled as follows:
First Blank: 10
Second Blank: 5
Final expression with blanks filled:
10√5 + 3√45 = 13√5.
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