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The problem is to simplify the expression $3\sqrt{2} + 5\sqrt{2} - 7\sqrt{3} + 4\sqrt{3}$.

ArithmeticSimplificationRadicalsSquare RootsExpression Manipulation
2025/3/30

1. Problem Description

The problem is to simplify the expression 32+52−73+433\sqrt{2} + 5\sqrt{2} - 7\sqrt{3} + 4\sqrt{3}.

2. Solution Steps

We can combine like terms in the expression.
Combine the terms with 2\sqrt{2}:
32+52=(3+5)2=823\sqrt{2} + 5\sqrt{2} = (3+5)\sqrt{2} = 8\sqrt{2}
Combine the terms with 3\sqrt{3}:
−73+43=(−7+4)3=−33-7\sqrt{3} + 4\sqrt{3} = (-7+4)\sqrt{3} = -3\sqrt{3}
Therefore, the simplified expression is 82−338\sqrt{2} - 3\sqrt{3}.

3. Final Answer

The final answer is 82−338\sqrt{2} - 3\sqrt{3}.

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