Problem 1: 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 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
 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 into three parts
 First number (FN) : 33
 Second number (SN): 076
 The 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 one’s 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 (TNFP)
 3*(1^2)*SP= Second digit of (1611) = Second digit of 160 = 6
 3*(1^2)*SP=6
 SP=6/3=2
3 2 1
 Finally, the cube root of (33076161)⅓ is 321
2. Finding the fourth root of 279841
 First, find the square root of the number 279841
 The square root of 279841 is 529
 Again find the square root of 529
 The 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

Problem2: 55555+5555+555+55+5+=?
To find the solution in an easy way first we have to count the no.of digits in a number and we have to choose the highest digit number
Step1: In this number 55555, the no.of digits are 5
5555=4
555=3
55=2
5=1
Step 2: Multiply as shown in the below
5*5=25 here 5 is the number and 2 is carried
5*4=20 add the previous carry to the number 20 then 20+2=22 2 is the number and 2 is carried
5*3=15 add the previous carry to the number 15 then 15+2=17 7 is the number and 1 is carried
5*2=10 add the previous carry to the number 10 then 10+1=11 1 is the number and 1 is carried
5*1=5 add the previous carry to the number 10 then 5+1=6 so 6 is the number
And finally, the answer is 61725.
Number

digit* no.of digits

sum

Carry Forward (CF)

sum+CF

Final Digit

55555

5*5

25

0

25

5

5555

5*4

20

2

22

2

555

5*3

15

2

17

7

55

5*2

10

1

11

1

5

5*1

5

1

6

6

Final Digit = second digit of (sum+CF)
Carry Forward = first digit of previous (sum+CF)
So the Final sum is 61725
Problem 3: 0.4444+0.444+0.44+0.4=?
To find the solution for this there is a shortcut which is similar to the above problem
Here we have to choose the smallest digit number
The smallest digit is 0.4 the no.of digits are 1
0.44=2
0.444=3
0.4444=4
Step 2: multiply as shown in the below
4*1=4
4*2=8
4*3=12 here 2 is the number and 1 is carried
4*4=16 add the previous carry to the number 16 then 16+1=17
And finally, we get 17284
After four digits there is a decimal point so the answer is 1.7284
Number

digit* no.of digits

sum

Carry Forward (CF)

sum+CF

Final Digit

0.4

4*1

4

0

4

4

0.44

4*2

8

0

8

8

0.444

4*3

12

1

2

2

0.4444

4*4

16

1

17

17

Final Digit = Second digit of (sum+CF)
Carry Forward = First digit of previous (sum+CF)
So the Final sum is 1.7284
Problem 4: 3333.666+33.6666+333.66+3.6=?
This can be divided into two parts
(3333+33+333+3)+(0.666+0.6666+0.66+0.6)
4 2 3 1 3 4 2 1
Part1 and 2 can solve by using the above method
Choose highest digit number choose the lowest digit number
3*4=12 2 is number 1 is carry 6*1=6
3*3=9 9+1=10 0 is number 1 is carry 6*2=12 2 is number and 1 is carry
3*2=6 6+1=7 6*3=18 18+1=19 9 is the number 1 is carry
3*1=3 6*4=24 24+1=25
Ans is 3702
ans is 2.5926
3702+2.5926=3704.5926
Trick: 61+16
When it is addition we have to multiply with 11
11*(1+6) or 11*(6+1)
11*7=77
Trick: 7667
When it is subtraction we have to multiply with 9
9(76)
9*1=9
Problem: 53+355665+63+369889=?
53+35(56+65)+63+36(98+89)
11(811+917)
11*11
121
Problem: 5335+8338+6886=?
9(2+52)
9*5=45
Trick: 65*75
1.7+1=8
2.6*8=48
3.difference between 6 and 7 is 1
4.last digit is 25
5.4825+1*50
=4825+50
=4875
Example: 25*95
9+1=10
2*10=20
2025
Difference between 2 and 9 is 7
2025+7*50
2025+350
2375