Home
Class 8
MATHS
Find the value of: (47)^(3)...

Find the value of:
`(47)^(3)`

A

103822

B

103823

C

103824

D

103825

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of \( (47)^3 \) using the shortcut method, we can apply the formula for the cube of a binomial. Here are the steps: ### Step-by-Step Solution: 1. **Rewrite 47**: We can express 47 as \( 40 + 7 \). 2. **Use the Binomial Cube Formula**: The formula for the cube of a sum \( (a + b)^3 \) is given by: \[ a^3 + b^3 + 3a^2b + 3ab^2 \] Here, \( a = 40 \) and \( b = 7 \). 3. **Calculate \( a^3 \)**: \[ 40^3 = 64000 \] 4. **Calculate \( b^3 \)**: \[ 7^3 = 343 \] 5. **Calculate \( 3a^2b \)**: \[ 3 \times (40^2) \times 7 = 3 \times 1600 \times 7 = 33600 \] 6. **Calculate \( 3ab^2 \)**: \[ 3 \times 40 \times (7^2) = 3 \times 40 \times 49 = 5880 \] 7. **Combine All Parts**: Now we can add all these values together: \[ 64000 + 343 + 33600 + 5880 \] 8. **Perform the Addition**: - First, add \( 64000 + 343 = 64343 \) - Next, add \( 64343 + 33600 = 97943 \) - Finally, add \( 97943 + 5880 = 103823 \) Thus, the value of \( (47)^3 \) is \( 103823 \).
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CUBES AND CUBE ROOTS

    RS AGGARWAL|Exercise Exercise 4C|18 Videos
  • CUBES AND CUBE ROOTS

    RS AGGARWAL|Exercise Exercise 4D|10 Videos
  • CUBES AND CUBE ROOTS

    RS AGGARWAL|Exercise Exercise 4A|10 Videos
  • CONSTRUCTION OF QUADRILATERALS

    RS AGGARWAL|Exercise Test Paper-17 (E)|1 Videos
  • DATA HANDLING

    RS AGGARWAL|Exercise Exercise 21C|11 Videos

Similar Questions

Explore conceptually related problems

If x^(4)+(1)/(x^(4))=47, find the value of x^(3)+1/x^(3)

If x^(4)+(1)/(x^(4))=47, Find the value of x^(3)+(1)/(x^(3))

Knowledge Check

  • Find the value of (sin43^(@))/(cos47^(@)) .

    A
    0
    B
    1
    C
    `sin43^(@)`
    D
    `cos47^(@)`
  • Find the value of tan4^(@).tan43^(@).tan47^(@).tan86^(@) .

    A
    0
    B
    1
    C
    `sqrt(3)`
    D
    `(1)/(sqrt(3))`
  • Find the square of 47 86

    A
    `4309`
    B
    `2203`
    C
    `2209`
    D
    `4209`
  • Similar Questions

    Explore conceptually related problems

    If a^(4)+(1)/(a^(4))=47 then find the value of a+(1)/(a) .

    Find the value of a^3 + b^3 + c^3 - 3abc if a + b + c = 12 and ab + bc + ca = 47 .

    If x^(4)+(1)/(x^(4))=47 find the value of x^(3)+(1)/(x^(3))

    Find the value of tan 4^@ tan 43^@ tan 47 ^@ tan 86 ^@

    What is the value of [(6.5)^(3)+(4.7)^(3)]div[(6.5)^(2)-6.5xx4.7+(4.7)^(2)]?