Calculate $101^3$ Value
To find the value of $101^3$, we can use the algebraic identity for the cube of a binomial: $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$. Let $a=100$ and $b=1$. This method simplifies the calculation.
Step-by-Step Calculation
-
Apply the binomial cube identity:
$101^3 = (100 + 1)^3$
-
Substitute $a=100$ and $b=1$ into the formula:
$ (100)^3 + 3(100)^2(1) + 3(100)(1)^2 + (1)^3 $
-
Calculate each term:
- $a^3 = 100^3 = 1,000,000$
- $3a^2b = 3 \times (100)^2 \times 1 = 3 \times 10,000 \times 1 = 30,000$
- $3ab^2 = 3 \times 100 \times 1^2 = 3 \times 100 \times 1 = 300$
- $b^3 = 1^3 = 1$
-
Sum the results:
$ 1,000,000 + 30,000 + 300 + 1 = 1,030,301 $
The value of $101^3$ is $1,030,301$.
Similar Questions
- Find the least number by which 6250 should be multiplied, so that it becomes a perfect cube.
- Find the smallest natural number N such that the product $288 \times N$ is a perfect cube.
- The square root of 18769 consists of how many digits?
- The square root of $1\frac{11}{25}$ is:
- The value of $\sqrt{142884}$ is:
- The number by which 62557 can be divided to make it a perfect cube is:
- What is the value of $99^3$?
- The value of $\sqrt[5]{\frac{32}{243}}$ is ________.
- The cube root of 250 lies between:
- The cube root of 150 will lie between:
Important Questions from Cube and Cube Root
If 5 \(\sqrt{3}\) + \(\sqrt{75}\) = 17.32, then the value of 14 \(\sqrt{3}\) + \(\sqrt{108}\) is:
Find the value of (25)3 + (-29)3 + (4)3
The value of \(\frac{\sqrt[3]{-2744} \times \sqrt[3]{-216}}{\sqrt[3]{\frac{64}{729}}}\) is:
A number is cube of 53. When 7 times of 57 is subtracted from the number, then the resultant number which is formed will be divisible by:
The sum of a positive number and its cube is 1740. What is the value of the number?
