Problem

Evaluate the expression \( 2\sqrt{8} + 3\sqrt{18} \)

Answer

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Answer

Since the square roots are the same, we can add the coefficients together. The simplified expression is then \( (4+9)\sqrt{2} \)

Steps

Step 1 ：First, simplify the radicands (the numbers under the square root symbols). Since 8 is equal to \(4*2\), we can simplify \(\sqrt{8}\) to \(2\sqrt{2}\). Similarly, since 18 is equal to \(9*2\), \(\sqrt{18}\) can be simplified to \(3\sqrt{2}\)

Step 2 ：So, the expression simplifies to \( 2*2\sqrt{2} + 3*3\sqrt{2} \)

Step 3 ：Which further simplifies to \( 4\sqrt{2} + 9\sqrt{2} \)

Step 4 ：Since the square roots are the same, we can add the coefficients together. The simplified expression is then \( (4+9)\sqrt{2} \)

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