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Mathematics

Assertion (A) : 121361=1119×1119=1119\sqrt{\dfrac{121}{361}} = \sqrt{\dfrac{11}{19} \times \dfrac{11}{19}} = \dfrac{11}{19}

Reason (R) : The square root of a number n is that number which when multiplied by itself gives n as the product.

  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.

Sq & Sq Roots

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Answer

We know that,

The square root of any number n is that number which when multiplied by itself gives n as the product.

⇒ n2=n×n=n\sqrt{n^2} = \sqrt{n \times n} = n

So, reason (R) is true.

Solving,

⇒121361⇒1119×1119⇒112192⇒112192⇒1119\Rightarrow \sqrt{\dfrac{121}{361}}\\[1em] \Rightarrow \sqrt{\dfrac{11}{19} \times \dfrac{11}{19}}\\[1em] \Rightarrow \sqrt{\dfrac{11^2}{19^2}}\\[1em] \Rightarrow \dfrac{\sqrt{11^2}}{\sqrt{19^2}}\\[1em] \Rightarrow \dfrac{11}{19}

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

Hence, option 1 is the correct option.

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