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Class 10MathematicsPolynomialsIrrational numbers and real numbersExpertLevel 27
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Which option is a correct counterexample showing that (\sqrt{a+b}=\sqrt{a}+\sqrt{b}) is false?

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Answer and explanation

Correct answer: (a=9) and (b=16)

(\sqrt{9+16}=5) while (\sqrt{9}+\sqrt{16}=7). In exams do not split addition inside a radical.

Related tags

Common-ErrorSquare-Root-RulesCounterexample

Frequently asked questions

What is the correct answer to this question?

(a=9) and (b=16)

Why is this the correct answer?

(\sqrt{9+16}=5) while (\sqrt{9}+\sqrt{16}=7). In exams do not split addition inside a radical.

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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  1. 1Which number is an irrational number?
  2. 2Which number is a rational number?
  3. 3All rational and irrational numbers together form which set?
  4. 4What type of number is the decimal 0.333...?
  5. 5The decimal \(0.1010010001\ldots\) that shows no fixed repeating block is what type of number?
  6. 6What type of number is \(\sqrt{49}\)?
  7. 7Which statement is correct about √11?
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  9. 9What is the decimal expansion of an irrational number like?
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