Question

Find the cube root of 27 by prime factorisation method​

Answer 1

Answer:

Step-by-step explanation:

27 = 3×3×3

Now square of any number is multiplication of the number by itself. Again, root of any number is half of square

And cube of any number is mulpile of same number by its square. Similarly cube root of any number is one-third of that original number in power.

Eg. Square of 2 =  22  

And Square Root of 4 =  √(2∗2)  

Now, 27 = 3*3*3

Therefore, √27 = √(3*3*3) = 3√3

Now, 2 3=2×2×2=8and(2×2×2)1/3=23/3=21=2  

Now, 3 comes up independently because there exists a square term inside the root but √3 doesn't gives any finite value because this number is not multiplied by another 3.

So we have to write it as 3√3.

And for (27) 1/3=31=3  

However we can find value of √3 using Lagrange Interpolation formula.

Hope it helped

Answer 2

Answer:

27 = 3×3×3

Now square of any number is multiplication of the number by itself. Again, root of any number is half of square

And cube of any number is mulpile of same number by its square. Similarly cube root of any number is one-third of that original number in power.

Eg. Square of 2 =  22  

And Square Root of 4 =  √(2∗2)  

Now, 27 = 3*3*3

Therefore, √27 = √(3*3*3) = 3√3

Now, 2 3=2×2×2=8and(2×2×2)1/3=23/3=21=2  

Now, 3 comes up independently because there exists a square term inside the root but √3 doesn't gives any finite value because this number is not multiplied by another 3.

So we have to write it as 3√3.

And for (27) 1/3=31=3  

Step-by-step explanation: