What is the value of \(\left(\sqrt{17}+\sqrt{8}\right)\left(\sqrt{17}-\sqrt{8}\right)-\sqrt{81}\)?
Answer and explanation
Correct answer: 0
Use the conjugate-product identity \((a+b)(a-b)=a^2-b^2\). Thus, \((\sqrt{17}+\sqrt{8})(\sqrt{17}-\sqrt{8})=17-8=9\). Also, \(\sqrt{81}=9\), so the complete expression is \(9-9=0\). Exam tip: Identify conjugate pairs first and apply the difference-of-squares identity instead of expanding the radicals term by term.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
Use the conjugate-product identity \((a+b)(a-b)=a^2-b^2\). Thus, \((\sqrt{17}+\sqrt{8})(\sqrt{17}-\sqrt{8})=17-8=9\). Also, \(\sqrt{81}=9\), so the complete expression is \(9-9=0\). Exam tip: Identify conjugate pairs first and apply the difference-of-squares identity instead of expanding the radicals term by term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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