Which statement about \((\sqrt{2}+\sqrt{8})\) is correct?
Answer and explanation
Correct answer: It is \(3\sqrt{2}\)
\(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\). Therefore, \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Option B results from incorrectly combining the numbers inside different radicals, while options C and D give an incorrect value or only \(\sqrt{8}\). Exam tip: square-root terms can be added or subtracted like algebraic terms only when their radicands are the same after simplification.
Frequently asked questions
What is the correct answer to this question?
It is \(3\sqrt{2}\)
Why is this the correct answer?
\(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\). Therefore, \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Option B results from incorrectly combining the numbers inside different radicals, while options C and D give an incorrect value or only \(\sqrt{8}\). Exam tip: square-root terms can be added or subtracted like algebraic terms only when their radicands are the same after simplification.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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