Which of the following is the value of \(4\sqrt{7}-\sqrt{112}\)?
Answer and explanation
Correct answer: \(0\)
\(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\). Hence \(4\sqrt{7}-\sqrt{112}=4\sqrt{7}-4\sqrt{7}=0\). Option A is correct. A tempting distractor is \(\sqrt{7}\), but it is not equal because the subtraction yields zero after simplifying \(\sqrt{112}\). Exam tip: always factor out perfect square factors from square roots to simplify surds quickly.
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
\(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\). Hence \(4\sqrt{7}-\sqrt{112}=4\sqrt{7}-4\sqrt{7}=0\). Option A is correct. A tempting distractor is \(\sqrt{7}\), but it is not equal because the subtraction yields zero after simplifying \(\sqrt{112}\). Exam tip: always factor out perfect square factors from square roots to simplify surds quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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