Square root in 3 seconds - math trick

tecmath
24 Mar 201509:45

TLDRIn this video, the Techmath channel teaches a quick method to calculate square roots of numbers, specifically focusing on perfect squares below 100. The method uses known squares up to 9 and emphasizes identifying the correct units digit of the result. Through examples, the video shows how to narrow down the possible answers and select the correct one based on the number's properties. The trick becomes faster with practice, and the video offers several examples to try. The host also promises future videos on calculating squares of any number using a different technique.

Takeaways

  • 🧠 The video introduces a quick method to find the square root of perfect squares under 100 in seconds.
  • 🔢 Example provided: The square root of 576 can be quickly calculated as 24 using this method.
  • 🧮 The technique requires knowledge of squares from 1 to 9, which is essential for this trick.
  • 📏 The last digit of the number determines potential ending digits of the square root, using squares like 16 and 36 for guidance.
  • ✂️ The first digit of the result is determined by looking at the largest square number less than the remaining digits of the original number.
  • 🔍 A comparison method is used to decide the final digit of the square root by comparing it to the nearest square.
  • ⏱️ Practicing this technique can help calculate square roots quickly and accurately over time.
  • 🧩 This trick is applicable mainly for perfect squares and requires some practice to master.
  • 📐 Example walkthroughs include finding square roots of numbers like 1,849 (43) and 3,364 (58).
  • 🔄 The method relies on mental math, involving multiplication and comparison to get faster with practice.

Q & A

  • What is the main purpose of the video?

    -The video teaches a trick for quickly calculating the square root of numbers, particularly focusing on perfect squares under 100.

  • How does the method work for determining the square root of a number like 576?

    -First, you check the units digit (6) and find possible square roots (4 and 6). Then, you look at the remaining digits (5 in this case) and find the square root that comes closest but doesn't exceed the number (2 for 4). Finally, you multiply the first digit (2) by the next number (3), and if the result is larger than the original first digit, you pick the smaller final digit.

  • Why is it important to consider both positive and negative square roots?

    -Because both positive and negative numbers, when squared, give the same result. For example, both 24 and -24 squared equal 576.

  • Why does the video focus on memorizing squares of numbers up to 9 or 10?

    -Memorizing squares up to 9 or 10 helps in quickly identifying possible values for the square root of larger numbers during calculations.

  • What is the significance of the complementary numbers in the trick?

    -Complementary numbers, such as 3 and 7 or 2 and 8, are helpful because their squares end with the same digit, making it easier to determine the last digit of the square root.

  • How does the method handle large numbers like 1,849?

    -For larger numbers, the method first looks at the last digit (9, giving possibilities of 3 or 7) and then the next digits (18, which is just above 16). The first digit of the square root is 4. By checking the next multiple of 4, it’s confirmed that the square root ends in 3, giving 43 as the final answer.

  • What role does multiplying by the next number play in the method?

    -Multiplying the first part of the answer by the next integer helps determine whether the answer will end in the smaller or larger digit option (e.g., 24 or 26).

  • What trick is suggested to handle numbers like 2025?

    -When the last digit is 5, there’s no need to calculate the last digit separately since it’s always 5. Then, the method proceeds with finding the first digit of the square root.

  • How does the method help improve speed in calculating square roots?

    -The method combines memorization of square values with quick checks of digits, reducing the need for lengthy calculations and allowing the user to quickly identify the square root.

  • What should viewers do to become faster at calculating square roots?

    -The video recommends practicing the method with different numbers and gradually speeding up as the process becomes more intuitive.

Outlines

00:00

🧮 Quick Square Root Calculation Trick

This paragraph introduces the video on the TechMath channel, focusing on a method to quickly calculate the square root of numbers, particularly perfect squares less than 100. The video begins with an example: finding the square root of 576, which results in ±24. The importance of recognizing both the positive and negative roots is emphasized, with the example demonstrating the method step-by-step. The explanation involves recognizing squares up to 9 and using these to deduce the square root quickly. The strategy includes analyzing the unit digits and the value of the remaining digits to determine the possible square roots.

05:01

🔢 Applying the Square Root Trick with Examples

The paragraph dives into more examples to solidify the trick of calculating square roots. It demonstrates the process with numbers like 1,849 and 3,364, explaining how to find the last digit's potential values and determine the correct square root. The examples highlight the technique of identifying whether the final digit will be a higher or lower number by multiplying the number's root and comparing it with the remaining digits. This section illustrates the method's efficiency and encourages practice to enhance speed and accuracy. The presenter also shows the unique case of a number ending in 5, where only one possible ending exists, simplifying the process.

Mindmap

Keywords

💡Square Root

A square root is a value that, when multiplied by itself, gives the original number. In the video, the host explains a method to quickly calculate square roots of perfect squares. For example, the square root of 576 is 24, as 24 * 24 equals 576.

💡Perfect Square

A perfect square is an integer that is the square of another integer. In the video, perfect squares less than 100 are referenced frequently as part of a quick calculation trick for square roots, such as 1, 4, 9, 16, and so on.

💡Positive or Negative Answer

When calculating square roots, there are always two possible results: a positive and a negative value, because both positive and negative numbers, when squared, yield the same product. In the video, the host reminds the viewers that both positive and negative answers are technically correct for square roots.

💡Units Digit

The units digit is the last digit of a number. In the trick demonstrated in the video, the units digit is used to narrow down the possible values of the square root. For example, if the units digit of a number is 6, the square root could end in either 4 or 6.

💡Crossing Out Digits

In the method demonstrated, crossing out the last two digits of the number helps isolate the portion of the number that is useful for estimating the first digit of the square root. This is part of the process of breaking down large numbers to make the calculation easier.

💡Multiplication of First Digit

This step involves multiplying the first digit of the square root estimate by the next higher integer. For example, if the first digit is 2, multiply it by 3. This helps determine whether to choose the lower or higher ending digit (e.g., 24 or 26 for the square root of 576).

💡Comparison with Remaining Number

In the trick, the result of the multiplication step is compared with the number formed by the remaining digits. This comparison helps decide whether the square root ends in a lower or higher number. For example, if the remaining number is less than the product of the multiplication, the smaller option is chosen.

💡Practice

The host emphasizes that with practice, one can quickly and accurately calculate square roots using this method. Repeated practice improves speed and helps avoid mistakes, as demonstrated with multiple examples in the video.

💡Complementary Numbers

Complementary numbers refer to two numbers that add up to 10. In the video, the host points out that the units digits of perfect squares often follow this pattern, which helps in narrowing down the possible square roots.

💡Estimation

Estimation is a key part of the trick, especially when identifying the first digit of the square root. By identifying the nearest perfect square below the number, the first digit of the square root can be estimated, significantly simplifying the process.

Highlights

Introduction to square root calculation for numbers less than 100.

Example: Finding the square root of 576 quickly.

Correct answer for the square root of 576 is positive or negative 24.

Importance of identifying both positive and negative square roots.

Explanation of how to calculate square roots using known squares.

Step-by-step process for finding the square root of 576.

Another example using the number 1849, with a focus on the unit digits.

Square root of 1849 is determined to be 43.

Example of finding the square root of 3364, with answer 58.

Process for calculating square root of 2025, with answer 45.

Further practice example using the number 5184, with answer 72.

Example of finding the square root of 1444, yielding 38.

Final example with 8281, calculated to be 91.

Encouragement to practice and improve speed of square root calculations.

Upcoming video topics: calculating squares of any number.

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