the smallest number by which Root over 27 should be multiplied so as to get a rational number is
Answers
Given:
A number √27.
To Find:
The simplest number is multiplied with the above number such that it becomes rational.
Solution:
The given problem can be solved using the concepts of rationalization.
1. The given number is √27.
2. The number √27 can also be written as,
= > √27 = √ (3 x 3 x 3) (Since, 27 can be written as 3 x 3).
= > √27 = √9 x √3 (Since √ (a x b) can be also written as √a x √ b).
= > √27 = 3 x √3 (Since 9 is a perfect square root of 3, √9 = 3).
= > √27 = 3√3.
3. The number 3√3 is irrational. The smallest number which is multiplied by 3√3 such that the number becomes rational is the smallest number that makes the number √3 rational.
4. The smallest number that can make the number √3 rationale is √3 itself.
5. Therefore, the number 3√3 when multiplied by √3 becomes 3 x 3 = 9. 9 is a rational number.
Therefore, the smallest number that can be multiplied by √27 to convert it into a rational number is √3.
Answer:
√3 is the answer....Bcs √27×√3 gives 81 and it is a rational number....