What is the value of 18^2 + 19^2?
Answer and explanation
Correct answer: 685
18^2 = 324 and 19^2 = 361, so 324 + 361 = 685. Alternatively use the formula for consecutive squares: \(n^2+(n+1)^2=2n(n+1)+1\). With n = 18, \(2\times18\times19+1=684+1=685\). A close distractor like 675 typically arises from an arithmetic slip computing one of the squares. Exam tip: use the consecutive-square formula to avoid calculation errors under time pressure.
Frequently asked questions
What is the correct answer to this question?
685
Why is this the correct answer?
18^2 = 324 and 19^2 = 361, so 324 + 361 = 685. Alternatively use the formula for consecutive squares: \(n^2+(n+1)^2=2n(n+1)+1\). With n = 18, \(2\times18\times19+1=684+1=685\). A close distractor like 675 typically arises from an arithmetic slip computing one of the squares. Exam tip: use the consecutive-square formula to avoid calculation errors under time pressure.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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