What is the value of (\!22^2+23^2\!)?
Answer and explanation
Correct answer: 1013
Direct calculation: \(22^2=484\) and \(23^2=529\). Adding gives \(484+529=1013\).
Alternate quick method (identity): \(a^2+b^2=(a+b)^2-2ab\). So \((22+23)^2-2\times22\times23=45^2-1012=2025-1012=1013\.
Exam tip: Use this identity for fast mental calculation of sums of squares. Option B (1003) is a common slip (off by 10) and therefore incorrect.
Frequently asked questions
What is the correct answer to this question?
1013
Why is this the correct answer?
Direct calculation: \(22^2=484\) and \(23^2=529\). Adding gives \(484+529=1013\).
Alternate quick method (identity): \(a^2+b^2=(a+b)^2-2ab\). So \((22+23)^2-2\times22\times23=45^2-1012=2025-1012=1013\.
Exam tip: Use this identity for fast mental calculation of sums of squares. Option B (1003) is a common slip (off by 10) and therefore incorrect.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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