# Determination of Square Root Shortcut Trick By The Math Boy

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Determination of Square Root Shortcut Trick

So today we will Know some unknown magical number.

The magical numbers are 1,4,6,9,6,5

Contents

#### Because** 1 square is 1,9 square is 81 of 1 **

** 2 square is 4, 8 square is 64 of 4 **

** 3 square is 9,7 square is 49 of 9 **

** 4 square is 16 of 6,6 square is 36 of 6**

** 5 square is 25 of **

#### Instructions:

1.Number must be a perfect square.

• You must know the number of squares from 1 to 9. Thus we know:

• If the last digit of a number is 1, the last digit of its square root must be 1 or 9.

• If the last digit is a number of 4, the last digit of its square root must be 2 or 8.

• If The last digit is a number of 5, the last digit of its square root must be 5 only.

• If the last digit is a number of 6, the last digit of its square root must be 4 or 6.

• If the last digit is a number, the last digit of its square root must be 3 or 7.

#### To find any of the square root Following are the steps below:

1. First split number into LHS and RHS. RHS = the last two digits and LHS is the other digits. (for example in 1024, RHS = 24, LHS = 10)

2. Now take LHS and from the list of squares (1 to 9), take the square root number just smaller than LHS. (Here LHS = 10. As 10 is just greater than 9 and less than 16 so we will pick a smaller number of square root. (Square root is 9 is 3).

3. This is our left side digit of answer. ) = 3

4. Now the last digit of the digit is 4 so the last digit of the square root must be 2

or 8.

5. Now multiply (Answer 1) with one higher digit and compare with LHS (3 4 = 12> 10).

6. If LHS <answer, we will choose smaller number or bigger number. {As 10 <12 we will choose 2 as the last digit between 2 and 8). (Answer 2) = 2 7. Now append (Answer 2) after (Answer 1) = 32. Final Answer. Follow the following to understand it better:

**EXAMPLE 1: Find square root of 576**

Step – 1 => Here RHS = 76, LHS = 5

Step – 2 => 5 is more than 4 but less than 9, so we will take square root of 4 = 2

Step – 3 => **(Answer 1) = 2.** This is our left side digit of the answer.

Step – 4 => Now as the last digit is 6, the last digit of the square root must be either 4 or 6.

Step – 5 => Now 2 3 = 6> 5. (multiplying (answer 1) by higher digits and comparing with LHS).

Step – 6 => As 5 is less than 8 we will choose **4 as right hand side digit of answer (answer 2)** LHS answer so smaller number).

Step – 7 => Append (Answer 2) after (Answer 1) = 24

**Hence square root of 576 Is = 24. (Ans)**

**EXAMPLE 2: _ Find square root of 7744**

Step – 1 => Here RHS = 44, LHS = 77

Step – 2 => 77 is more than 64 but less than 81, so we will take square root of 64 = 2

step – 3 = > **(Answer 1) = 8.** This is our left side digit of the answer.

Step – 4 => Now as the last digit is 4, the last digit of the square root is Fmust either 2 or 8,

Step – 5 => Now 1 * 9 = 72 <77. (multiplying (answer 1) by higher digits and comparing with LHS)

Step – 6 => As77 is greater than 72 we will choose** 8 as right hand side digit of answer (answer: 2).** (LHS <answer so smaller number).

Step – 7 => Append (answer 2) after (answer 1) = 88

** Hence the square root of 7744 is = 88. (Ans)**