Home
Class 8
MATHS
The least number to be multiplied with 9...

The least number to be multiplied with 9 to make it a perfect cube is _______________.

Text Solution

AI Generated Solution

The correct Answer is:
To find the least number that needs to be multiplied with 9 to make it a perfect cube, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the given number**: The number we have is 9. 2. **Prime factorization of 9**: - The prime factorization of 9 is \( 3^2 \) (since \( 9 = 3 \times 3 \)). 3. **Understanding perfect cubes**: - A number is a perfect cube if all the exponents in its prime factorization are multiples of 3. - For example, \( 27 = 3^3 \) is a perfect cube, but \( 9 = 3^2 \) is not. 4. **Determine the required exponent**: - The exponent of 3 in the factorization of 9 is 2. - To make it a perfect cube, we need the exponent to be a multiple of 3. The nearest multiple of 3 greater than 2 is 3. 5. **Calculate the difference**: - To go from \( 2 \) to \( 3 \), we need to add \( 1 \) to the exponent of 3. - This means we need one more factor of 3. 6. **Find the least number to multiply**: - Therefore, the least number that needs to be multiplied with 9 is \( 3^1 = 3 \). 7. **Final result**: - When we multiply \( 9 \) by \( 3 \), we get \( 27 \), which is \( 3^3 \) and thus a perfect cube. ### Conclusion: The least number to be multiplied with 9 to make it a perfect cube is **3**. ---
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • SQUARE - SQUARE ROOT AND CUBE-CUBE ROOT

    NCERT EXEMPLAR|Exercise Solved Examples (state whether the statements are true (T) or false (F))|5 Videos
  • SQUARE - SQUARE ROOT AND CUBE-CUBE ROOT

    NCERT EXEMPLAR|Exercise Solved Examples |14 Videos
  • SQUARE - SQUARE ROOT AND CUBE-CUBE ROOT

    NCERT EXEMPLAR|Exercise Exercise |52 Videos
  • RATIONAL NUMBERS

    NCERT EXEMPLAR|Exercise Think and Discuss |1 Videos
  • UNDERSTANDING QUADRILATERALS AND PRACTICAL GEOMETRY

    NCERT EXEMPLAR|Exercise THINK AND DISCUSS|2 Videos

Similar Questions

Explore conceptually related problems

The least number by which 72 be multiplied to make it a perfect cube is _____________.

The least number by which 125 be multiplied to make it a perfect square is _____________.

Knowledge Check

  • What is the least number to be multiplied with 294 to make it a perfect square?

    A
    2
    B
    3
    C
    6
    D
    24
  • By what least number 3600 must be multiplied to make it a perfect cube?

    A
    60
    B
    50
    C
    300
    D
    450
  • The least number which should be multiplied to 243 to get a perfect cube is

    A
    6
    B
    9
    C
    2
    D
    3
  • Similar Questions

    Explore conceptually related problems

    The least number by which 72 be divided to make it a perfect cube is ______

    The least number to be added to 435 to make it a perfect square is?

    The smallest number with which 16 should be multipled to make it a perfect cube is __________

    BY what least number must 21600 be multiplied to make it a perfect cube?

    What least number should be multiplied to 245 to make it a perfect square?