Question
Evaluate the following : $(103)^3$
✓
Answer
We know that $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
$\Rightarrow (103)^3$ can be written as $(100 + 3)^3$
Here$, a = 100$ and $b = 3$
$(103)^3 = (100 + 3)^3$
$= (100)^3 + (3)^3 + 3(100)(3)(100 + 3)$
$= 1000000 + 27 + (900 \times 103)$
$= 1000000 + 27 + 92700$
$= 1092727$
The value of $(103)^3 = 1092727$
$\Rightarrow (103)^3$ can be written as $(100 + 3)^3$
Here$, a = 100$ and $b = 3$
$(103)^3 = (100 + 3)^3$
$= (100)^3 + (3)^3 + 3(100)(3)(100 + 3)$
$= 1000000 + 27 + (900 \times 103)$
$= 1000000 + 27 + 92700$
$= 1092727$
The value of $(103)^3 = 1092727$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Monica has a piece of Canvas whose area is $551\ m^2.$ She uses it to have a conical tent made with a base radius of $7\ m$. Assuming that all the stitching margins and wastage incurred while cutting, amounts to approximately $1\ m^2.$ Find the volume of the tent that can be made with it.
→Form the frequency distribution table and Find the mean of the marks obtained by $30$ students of Class $IX$ of a school, as given below:
$10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88$
→$10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88$
In the given figure, if AB || CD, $\angle$ APQ = 50° and $\angle$PRD = 127°, find x and y.
→Find the coordinates of the point:
- Which lies on x and y axes both.
- Whose ordinate is -4 and which lies on y-axis.
- whose abscissa is 5 and which lies on x-axis.
In the adjoining figure, CE || AD and CF || BA. Prove that $\text{ar}(\triangle\text{CBG})=\text{ar}(\triangle\text{AFG}).$
→Read the following bar graph and answer the following questions:
- What is the information given by the bar graph?
- State each of the following whether true or false.
- The number of government companies in 1957 is that of 1982 is 1 : 9.
- The number of government companies has decreased over the year 1957 to 1983.
Draw a histogram for the daily earning of 30 drug stores in the following table:
| Daily earning (in ₹): | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 |
| Number of stores: | 16 | 10 | 7 | 3 | 1 |
Factorize the following expressions: $1029 - 3x^3$
→A wall of length $10\ m$ was to be built across open ground. The height of wall is $4 \ m$ and the thickness of the wall is $24 \ cm$. If this wall is to be built up with bricks whose dimensions are $24\ cm\times 12\ cm\times 8\ cm.$ How many bricks would be required?
→Various modes of tansport used by 1850 students of a school are given below:
Draw a bar graph to represent the above data.
|
School bus
|
Private
|
Bicycle
|
Rickshaw
|
By foot
|
|
640
|
360
|
490
|
210
|
150
|