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Mathematics

Assertion (A) : 9683×13753=110\sqrt[3]{968} \times \sqrt[3]{1375} = 110

Reason (R) : If p and q are two whole numbers, then p3×q3=pq3\sqrt[3]{p} \times \sqrt[3]{q} = \sqrt[3]{pq}.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Cube & Cube Roots

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Answer

If p and q are two whole numbers, then p3×q3=p×q3=pq3\sqrt[3]{p} \times \sqrt[3]{q} = \sqrt[3]{p \times q} = \sqrt[3]{pq}.

So, reason (R) is true.

Solving,

⇒9683×13753⇒968×13753⇒13310003⇒110.\Rightarrow \sqrt[3]{968} \times \sqrt[3]{1375} \\[1em] \Rightarrow \sqrt[3]{968 \times 1375}\\[1em] \Rightarrow \sqrt[3]{1331000}\\[1em] \Rightarrow 110.

So, assertion (A) is true and reason (R) clearly explains assertion.

Hence, option 1 is the correct option.

Answered By

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