If u = 5 + \sqrt{2} and v = 5 - \sqrt{2}, what is the value of uv?
Answer and explanation
Correct answer: 23
These are conjugates, so use the difference of squares identity: \((a+b)(a-b)=a^2-b^2\). With \(a=5\) and \(b=\sqrt{2}\), \((5+\sqrt{2})(5-\sqrt{2})=5^2-(\sqrt{2})^2=25-2=23\). Option B (27) is incorrect — it confuses adding instead of subtracting the square; options C and D give irrational forms that are not the product. Exam tip: recognize conjugates and apply the difference of squares to compute such products quickly and reliably.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
These are conjugates, so use the difference of squares identity: \((a+b)(a-b)=a^2-b^2\). With \(a=5\) and \(b=\sqrt{2}\), \((5+\sqrt{2})(5-\sqrt{2})=5^2-(\sqrt{2})^2=25-2=23\). Option B (27) is incorrect — it confuses adding instead of subtracting the square; options C and D give irrational forms that are not the product. Exam tip: recognize conjugates and apply the difference of squares to compute such products quickly and reliably.
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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