Smallest Number to Be Multiplied with √27 to Get a Rational Number

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: The smallest number by which √27 should be multiplied so as to get a rational number is:

(a) √27    (b) 3√3    (c) √3    (d) 3

Step 1: Simplify √27

√27 = √(9 × 3)

√27 = 3√3

Step 2: Decide What to Multiply

To make the product rational, the irrational part √3 must be eliminated.

Multiplying by √3 gives:

3√3 × √3 = 3 × 3 = 9

which is a rational number.

Final Answer

✔ The smallest number required is √3.

✔ Correct option: (c) √3

Conclusion

Thus, multiplying √27 by √3 gives a rational number, and it is the smallest such number.