Question

Find cube root of 1001 by using binomial expansion?

Answer 1

3√10+1
it is the answer

Answer 2

Answer:

The answer is 10.0033

Step-by-step explanation:

$(1001)^{\frac{1}{3}}=(1000+1)^{\frac{1}{3}}\\\\=[1000^{\frac{1}{3}}(1+\frac{1}{1000})^{\frac{1}{3}}]\\\\=(10^3)^{\frac{1}{3}}(1+\frac{1}{1000})^{\frac{1}{3}})\\\\=10\cdot (1+\frac{1}{1000})^{\frac{1}{3}}\\\\\text{Now, Applying binomial theorem : }(a+b)^n= \sum_{k=0}^{n}\binom{n}{k}a^{n-k}\cdot b^k\\\\=10\cdot (1+\frac{1}{3}\times \frac{1}{1000})\\\\=10\times 1.00033\\\\=10.0033$

So, cube root of 1001 is 10.0033