Square Root Tricks
The value of a number’s square root is its power divided by two. It is the number whose product gives the initial number on its own. It is represented using the symbol √ . The number underneath the Square Root symbol is referred to as the radicand, and the symbol itself is referred to as a radical.
This is very simple topic of square root. We will discover how else to calculate the square root here.
To find square root first we have to know square of 1 to 10 number or we write down square of 1 to 10 number on paper, to make it easy.
It is as follow:-
Number |
Square of Number |
(1)2 |
1 |
(2)2 |
4 |
(3)2 |
9 |
(4)2 |
16 |
(5)2 |
25 |
(6)2 |
36 |
(7)2 |
49 |
(8)2 |
64 |
(9)2 |
81 |
(10)2 |
100 |
Than we make a square root table to find out square root in simple way.
Digits | First | Last |
3 | 1 | 1 |
4 | 2 | 1 |
5 | 3 | 1 |
6 | 4 | 1 |
7 | 5 | 1 |
8 | 6 | 1 |
1) If we want to find the square root of 3 digits than we will consider first and last number.
2) If we want to find the square root of 4 digits than we will consider first 2 digits and last number.
3) If we want to find the square root of 5 digits than we will consider first 3 digits and last number.
4) If we want to find the square root of 6 digits than we will consider first 4 digits and last number.
Like this we will go no increasing the first numbers as digits (radicand) will increase but last digit will be one digit always for square root.
Here are some examples: –
1) √121
This is 3 digits radicand, so here we will consider first and last number.
First number is 1 and last is also 1.
Now if we start from last digit than we just have to find 1 or smaller than 1 in the 1 to 10 table
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
In this table we see 1 two time that is (1)2 =1
And (9)2 =81 in 81 last number is 1
We will take the number that we have to find the square, so here we take 1 as it is square of 1, and 9 as 81 is the square of 9.
Soit is like this1 / 9
In the final answer last digit can be 1 or 9
Then we will take first digit it is 1 so again we have to find 1 or smaller than 1 in the 1 to 10 table
In this table we see 1 two time that is (1)2 =1
And (9)2 =81 in 81 last number is 1
We will take the number that we have to find the square, so here we take 1 as it is square of 1, and 9 as 81 is the square of 9.
So it is like this 11 and 99.
In square root we get two answers. By multiplication we can find out the right answer.
11 X 11=121 , 99 X 99= 9801
So final answer is 11.
2) √441
This is 3 digits radicand, so here we will consider first and last number.
First number is 4 and last is 1.
Now if we start from last digit than we just have to find 1 or smaller than 1 in the 1 to 10 table
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
In this table we see 1 two time that is (1)2 =1
And (9)2 =81 in 81 last number is 1
We will take the number that we have to find the square, so here we take 1 as it is square of 1, and 9 as 81 is the square of 9.
So it is like this 1 / 9
In the final answer last digit can be 1 or 9
Then we will take first digit it is 4 so we have to find 4 or smaller than 4 in the 1 to 10 table
In this table we see 4 in (2)2 =4
And (8)2 =64 in 64 last number is 4
We will take the number that we have to find the square, so here we take 1 as it is square of 1, and 8 as 64 is the square of 8.
Soit is like this 21 and 89.
In square root we get two answers. By multiplication we can find out the right answer.
21 X 21=441 , 89 X 89= 7921
So final answer is 21.
3) √841
This is 3 digits radicand, so here we will consider first and last number.
First number is 8 and last is 1.
Now if we start from last digit than we just have to find 1 or smaller than 1 in the 1 to 10 table
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
In this table we see 1 two time that is (1)2 =1
And(9)2 =81 in 81 last number is 1
We will take the number that we have to find the square, so here we take 1 as it is square of 1, and 9 as 81 is the square of 9.
So it is like this 1 / 9
In the final answer last digit can be 1 or 9
Then we will take first digit it is 8 so we have to find 8 or smaller than in the 1 to 10 table
In this table we do not find 8 so we see smaller number than 8that is 4,(2)2 =4
We will take the number that we have to find the square, so here we take 2 as it is square of 4,
So it is like this 21 and 29.
In square root we get two answers. By multiplication we can find out the right answer.
21 X 21=441
29 X 29= 841
So final answer is 29.
4) √3844
This is 4 digits radicand, so here we will consider first 2 digit and one digit from last.
Now if we start from last that is 4 we have to find same number or smaller than 4 in the 1 to 10 square table
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
In this table we find 4 two time that is (2)2 =4
And (8)2 =64 in 64 last number is 4
We will take the number that we have to find the square, so here we take 2 as it is square of 4, and 8 as 64 is the square of 8.
So it is like this 2 / 8
In the final answer last digit can be 2 or 8
Then we will take first two digits it is 38 so we have to find 38 or smaller than 38 in the 1 to 10 square table
In this table we do not find 38 so we see smaller number than 38, that is 36 (6)2 =36
So, we will take 6.
Now we are getting two figures
It is like this 62 and 68
By multiplication we can find out the right answer.
62 X 62=3844,68 X 68= 4624
So final answer is 62
5) √10404
This is 5 digits radicand, so here we will consider first 3 digit and one digit from last.
Now if we start from last that is 4 we have to find same number or smaller than 4 in the 1 to 10 square table
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
In this table we find 4 two time that is (2)2 =4
And (8)2 =64 in 64 last number is 4
We will take the number that we have to find the square, so here we take 2 as it is square of 4, and 8 as 64 is the square of 8.
So it is like this 2 / 8
In the final answer last digit can be 2 or 8
Then we will take first 3 digits it is 104 so we have to find 104 or smaller than 104 in the square table
In this table we do not find 104 so we see smaller number than104, that is 100 (10)2 =100
So, we will take 10.
Now we are getting two figures
It is like this 102 and 108
By multiplicationwe can find out the right answer.
102 X 102=10404, 108 X 108= 11664
So final answer is 102
6) √42436
This is 5 digits radicand, so here we will consider first 3 digit and one digit from last.
Now if we start from last that is 6 we have to find same number or smaller than 6 in the 1 to 10 square table
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
In this table we find 6 two time that is (4)2 =16 in this last number is 6
And (6)2 =36 in 36 last number is 6
We will take the number that we have to find the square, so here we take 4 as it is square of 16, and 6 as it is square of 36 .
So it is like this 4 / 6
In the final answer last digit can be 4 or 6
Then we will take first 3 digits it is 424 so we have to find 424 or smaller than 424 in the square table
In this table we do not find 424 so we see smaller number than 424, that is 400 (20)2 =400
Sowe will take 20.
Now we are getting two figures
It is like this 204 and 206
By multiplicationwe can find out the right answer.
204X 204=41616 ,206 X 206= 42436
So final answer is 206
7) √11025
This is 5 digits radicand, so here we will consider first 3 digit and one digit from last.
Now if we start from last that is 5.
So here we will get only one answer.
Number | Square of Number |
(1)2 | 1 |
(2)2 | 4 |
(3)2 | 9 |
(4)2 | 16 |
(5)2 | 25 |
(6)2 | 36 |
(7)2 | 49 |
(8)2 | 64 |
(9)2 | 81 |
(10)2 | 100 |
We will take 5 as a last digit of the answer.
Then we will take first 3 digits it is 110 so we have to find 110 or smaller than 110 in the square table
In this table we do not find 110 so we see smaller number than 110, that is 100 (10)2 =100
So we will take 10.
Now we are getting two figures
105
By multiplication we can find out the right answer.
105 X 105=11025
So final answer is 105