Problem: Simplify (33076161)^⅓ + (279841)^¼ + (243)^⅕ = ?

(33076161)^1/3 + (279841)^1/4 + (243)^1/5 = ?

Given options are

• 344
• 345
• 346
• 347
• None of these

The solution involves in four steps

• Finding the cube root of the number 33076161
• Finding the fourth root of 279841
• Find the fifth root of 243
• Adding all the three numbers

1. Finding the cube root of the number 33076161

TP   SP   FP - We will be finding the numbers in these three places as below.

• Divide the number in three parts
• First number (FN)   : 33
• Second number (SN) : 076
• Third number (TN) : 161

To find the cube root, we will use TN, then FN and finally SN.

• TN ends with 1, so the number in the ones place (FP) is 1. (Refer Table 1 below)

TP   SP   1

• FN is 33, which in between the cube of 3 and 4, so we have to choose the small number which is 3 will be in third place (TP). (Refer table 1 below)

3  SP  1

• To find the number in second place, we can use the formula - 3*(TP^2)*SP= second digit of (TN-FP)
• 3*(1^2)*SP= Second digit of (161-1) = Second digit of 160 = 6
• 3*(1^2)*SP=6
• SP=6/3=2

3  2  1

• Finally, cube root of (33076161)⅓ is 321

2. Finding the fourth root of 279841

• First find the square  root of the number 279841
• Square root of 279841 is 529
• Again find the square root of 529
• Square root of 529 is 23
• (23^4)¼=23

3. Find the fifth root of 243

• Rewrite 243 as 3^5
• Cancel the common factor of 5
• And the answer is 3

4. Then, the final step is adding all the three numbers 321+23+3=347

Table 1: Square, Cube, Numbers Ranging 0 - 10

Number x	Square x2	Cube x3
1	1	1
2	4	8
3	9	27
4	16	64
5	25	125
6	36	216
7	49	343
8	64	512
9	81	729
10	100	1000