QQuestionMathematics
QuestionMathematics
# Combine these radicals: $- 3 \sqrt{81}+\sqrt{16}$
A. - 23
B. - 11
C. $- 3 \sqrt{97}$
D. $- 3 \sqrt{13}$
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Answer
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Step 1:I'll solve this step by step, following the LaTeX formatting guidelines precisely:
Step 2:: Simplify \sqrt{81}
- $$\sqrt{81} = 9$$ (since $$9 \times 9 = 81$$)
Step 3:: Simplify \sqrt{16}
- $$\sqrt{16} = 4$$ (since $$4 \times 4 = 16$$)
Step 4:: Rewrite the original expression
- $$= -27 + 4
- = - 3(9) + 4
Step 5:: Perform final calculation
- $$= -23
Final Answer
Key insights: - Always simplify radicals first by finding perfect square roots - Multiply the coefficient with the simplified radical - Perform standard arithmetic operations - The problem tests understanding of radical simplification and basic arithmetic
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