Quotes and poetry by dania_jasrah

IMPROVE BASICS IN MATH

PERFECT SQUARES

It is not a wonder, that learning the perfect squares of numbers, will always help us to quickly solve questions. Now, it should be noted, that you should not only be able to find the square of a number, when its given, you should also be able to find the square root, when the perfect square is given. For non-perfect square numbers as well, there are easy methods to find answers. It is easy to solve questions when we have just a number and is asked to find the square root, but when it comes to its applications, it becomes complicated. But before that a few random tactics, most students know and follow :-

◆The unit's place.
If the unit's place of the perfect square has 1, then it's the root will have 1 or 9.
If the unit's place of the perfect square has 4, then it's the root will have 2 or 8.
If the unit's place of the perfect square has 9, then it's the root will have 3 or 7.
If the unit's place of the perfect square has 6, then it's the root will have 4 or 6.
If the unit's place of the perfect square has 5, then it's the root will have 5.

That's done. The most important application is Pythagoras Theorem which we all know, but keep these in mind,
◆100–64=36
◆100–36=64
◆64+36=100

◆9+16=25
◆81+144=225
◆144+25=169
◆576+49=625

Keeping these in mind you will be able to do most of the calculations easily. Now for numbers that are not perfect squares (link is in my bio), you may quickly go through the following trick for an approximate answer and it was not developed by me (ToT) – Please read caption

Let us take an example. Say 7
7 is between the perfect squares 4 and 9. Square root of 4 = 2 and that of 9 is 3. This means that the square root of 7 will be in between 2 and 3. Which means it will be 2. ___

For this do these calculations:
7–4 =3
9–4=5

3÷5 = 0.6
Ans = √7 ≈ 2 + 0.6 = 2.6

Another example 11
Between 9 and 16
√9=3 and therefore the answer will be 3. ___
11-9=2
16-9=7
2÷7=0.285
Answer = √11
≈3+0.285
=3.28 ≈ 3.3

◆Squares of numbers with 5 in units place
Example 25
5×5 =25 which we know
The other digit is 2
Next number 3
3×2 = 6
So 25×25=625

Example 75
5×5=25
The other digit is 7
Next number 8
7×8=56
So 75×75=5625

Example 105
5×5=25
The other digits taken together is 10
Next number 11
11×10=110
So 105×105=11025

Thank you

©daffodilpearlzz
05_01_2021