Math Tricks

Suppose you know the square of a number, say, 70; how to find square of 69 or 71?

Step 1 : (70*70) = 4900 (which you know already)

Step 2 : If the adjacent number is more then add  i.e. (71*71) = 4900 + (70 + 71) =  5041

Step 3 : If the adjacent number is less then minus  i.e. (69*69) = 4900 – (70 + 69) = 4761

Example  1 : 44/25

Step 1 : To make the denominator 100, multiply it with 4.

Step 2 : Means multiply with 4 the numerator and denominator to nullify the effect 44*4/(25*4)

Step 3 : 176/100 = 1.76 (It’s the final answer)

Example  1 : 64/125

Step 1 : To make the denominator 1000, multiply it with 8.

Step 2 : Means multiply with 8 the numerator and denominator to nullify the effect 64*8/(125*8)

Step 3 : 512/1000 = 0.512 (It’s the final answer)

Example  1 : 48 * 52

Step 1 : Here the two numbers are symmetrical to 50.

Step 2 : Means we can write (50 – 2) * (50 + 2)

Step 3 : 50Square – 2Sqaure = 2496

Step 6 : 2496(It’s the final answer)

Formula to find sum of n consecutive square numbers = n*(n+1)*(2n+1)/6

Step 1 : Find the sum of first 20 consecutive square numbers

Step 2 : n= 20

Step3 :n*(n+1)*(2n+1)/6 = 20*(20+1)*(2*20 +1)/6 = 20*21*41/6

Step 4 : 2870 (It’s the final answer)