What is the value of \((23^2+24^2)\)?
Answer and explanation
Correct answer: 1105
Direct method: \(23^2=529\) and \(24^2=576\). Adding gives \(529+576=1105\).
Alternate quick method: use \(a^2+b^2=(a+b)^2-2ab\). Here \((23+24)^2=47^2=2209\) and \(2\times23\times24=1104\), so \(2209-1104=1105\).
Why other options are wrong: 1100 and 1095 result from small arithmetic undercounts; 1115 is an overestimate.
Exam tip: Use the identity \((a+b)^2-2ab\) to avoid computing two large squares separately — it's faster and reduces errors.
Frequently asked questions
What is the correct answer to this question?
1105
Why is this the correct answer?
Direct method: \(23^2=529\) and \(24^2=576\). Adding gives \(529+576=1105\).
Alternate quick method: use \(a^2+b^2=(a+b)^2-2ab\). Here \((23+24)^2=47^2=2209\) and \(2\times23\times24=1104\), so \(2209-1104=1105\).
Why other options are wrong: 1100 and 1095 result from small arithmetic undercounts; 1115 is an overestimate.
Exam tip: Use the identity \((a+b)^2-2ab\) to avoid computing two large squares separately — it's faster and reduces errors.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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