A Maths Trick for Square of a number

This article is about Maths tricks for finding square of a number.It is not tough task to find square of a number but how fast we compute its value is a major consideration.
In this article i will discuss about some tricks for easy computation.
A logo to manage squares:

Friends,

Problem 1: What is square of number 10001?
Solution: For this type of number which is start from 1 and end by 1 and zeroes in between.
step:- Write 1 at first and at end and makes double the zeroes.
Square of 10001 is=10000001

Problem 2: What is square of number 10101?
solution:
Step 1: For this type of problem count the numbers of 1's.
Step2: Write from 1 to (number of 1's) and then reverse upto again 1 occurs and placed zero in between every digit.
Ex. square of 10101=?
step 1:Count number of 1's=3
step 2:Write from 1 to 3 and zero in between and reverse upto again 1 occurs
102030201

Problem 3:How to calculate 4²+5²+(4*5)²?
solution:For this type of problem when two number are continuous and third in its multiplication then ans is square of one greater then third number.
Ex.4 is first number and 5 is second number and 4*5 is third number then we can write it as:
4²+5²+20²=21²
we can say that the ans is=21²=441

Problem 4: How to calculate integers between square of two continuous numbers?
solution: Let two continuous numbers 6 and 7
Integers between 6² and 7²=?
We can calculate it by just add these two numbers and subtract 1 i,s 6+7-1=12
36 37 38 39 40 41 42 43 44 45 46 47 48 49

Problem 5: how can we add series of type 1+3+5+7+9
solution:
STEP 1:Count numbers.
Step 2:Find mid number and calculate its square.
If number is odd it is easy to calculate mid and when number is even then find average of two mids.
Ex. Add 1+3+5+7+9
step 1: numbers are 5.
step 2: 5 is mid number so ans is 5²=25
Ex2. When add 1+3+5+7+9+11=?
step 1: Numbers are 6.
step 2: Average of 5 and 7 is (5+7)/2=6 so ans is 6²=36

Mathematics........get faster

This article is about get speed in computation in mathematics.As all know fundamentals of mathematics but how fast one can solve any question takes more consideration.In this article a few tricks of solve maths is discuss in front of you.
Friends,
Problem:1: What is the unit place value for (2345)³=?
Ans. unit place value(5)³=125 so ans is=5

Problem:2: What is the unit place value for (2345)^1233=?
solution: unit place value(2345)¹²³³=?
step 1:First divide 1233 by 4 which is=308 and remainder=1
step 2:Unit place value(2345)¹²³³=(unit digit of number)^remainder
Answer is=5¹=5
Note:(number)⁰=1

Problem:3 What is value of (85)^2=?
Solution: step 1:When there we have to calculate square of number having unit digit 5 then
take square of 5=25 and (ten digit)*(ten digit+1)
Ans is=8*(8+1)25=7225
Friends,
These are only three types of questions.I will discuss more soon.........stay in touch.
Thank you.