Which of the following is the value of \(\sqrt[3]{216}+\sqrt[3]{125}\)?
Answer and explanation
Correct answer: 11
\(\sqrt[3]{216}=6\) and \(\sqrt[3]{125}=5\) because 216 and 125 are perfect cubes (6^3=216, 5^3=125). Therefore the sum is \(6+5=11\). Option D arises if one mistakenly takes the cube root after adding (\(\sqrt[3]{216+125}=\sqrt[3]{341}\) ), which is not the same; its value is about 6.99. Exam tip: identify perfect cubes first, take each cube root, then perform the required arithmetic—don’t swap root and sum operations.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
\(\sqrt[3]{216}=6\) and \(\sqrt[3]{125}=5\) because 216 and 125 are perfect cubes (6^3=216, 5^3=125). Therefore the sum is \(6+5=11\). Option D arises if one mistakenly takes the cube root after adding (\(\sqrt[3]{216+125}=\sqrt[3]{341}\) ), which is not the same; its value is about 6.99. Exam tip: identify perfect cubes first, take each cube root, then perform the required arithmetic—don’t swap root and sum operations.
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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