Squaring Tricks

**11 - 19**

- Square the ones digit. This becomes your last digit.
- Multiply the ones digit by 2. This becomes your second digit.
- Retain the tens digit (i.e., 1) and append the above results.

Example: \(17^{2}\)

- \(7^{2}=49\). The 9 is your last digit. Carry the 4 to the left.
- \(7 \times 2 = 14 \). The 4 plus the 4 remaining from the first step is your second digit, 8. As before carry the 1 to the left.
- Retain the 1 from "17", add to it the 1 remaining from the previous step, and you get 289.

**20 - 50**

- Subtract the number you want to square from 100. (100 - x)
- Take this difference and subtract it from the number you want to square. [x - (100 - x)]. This is the first 2 digits of your answer.
- Square the difference, the answer from step 1. This is the last 2 digits of your answer.

Example 1: \(96^{2}\)

- \(100 - 96 = 4 \)
- \(96 - 4 = 92\). First two digits of answer.
- \( 4^{2} = 16 \). Last two digits of answer. \(96^{2} = 9216\)

Example 2: \(88^{2}\)

- \(100 - 88 = 12\)
- \(88 - 12 = 76\). First two digits of answer.
- \(12^{2} = 144\). 44 are the last two digits. Carry the 1 over the 6 in previous result to obtain 7744.

**50 - 59**

- Square the tens digit and add to that the ones digit if your original number. That's the first two numbers of your answer.
- Square your ones digit. That's your last two numbers.

Example: \(54^{2}\)

- \( 5^{2} + 4 = 29 \). That's our first two numbers.
- \( 4^{2} = 16 \). That's our last two numbers. The answer is 2916.

**Numbers greater than 100**

- Subtract 100 from the number you want to square (x - 100).
- Take the difference and add it to the number you want to square. [x + (x - 100)]. This is the first 3 digits of your answer.
- Square the difference, the answer from step 1. This is the last 2 digits of your answer.

Example: \(112^{2}\)

- \(112 - 100 = 12\)
- \(112 + 12 = 124 \). First three digits of answer.
- \( 12^{2} = 144 \). Carry the 1 over the 4. Answer: 12,544

**Numbers around 1000**

- Subtract 1000 from the number you want to square (x - 1000).
- Take the difference and add it to the number you want to square. [x + (x - 100)]. This is the first 4 digits of your answer.
- Square the difference, the answer from step 1. This is the last 3 digits of your answer.

Example 1: \(996^{2}\)

- \(1000 - 996 = 4 \)
- \(996 - 4 = 992\). First 3 digits.
- \(4^{2}= 16\). Last 3 digits. Answer: 992,016

Example 2: \(1007^{2}\)

- \(1007 - 1000 = 7 \)
- \(1007 + 7 = 1014\). First 4 digits.
- \(7^{2} = 49\). Last 3 digits. Answer: 1,014,049

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