Find Square Root by Hand without Calculator
TLDRIn this educational tutorial, viewers are guided through the process of manually calculating the square root of a non-perfect square number, specifically the number 38. The presenter begins by demonstrating that 38 cannot be perfectly squared by any whole number and proceeds to approximate its square root. The method involves setting up a division-like template, using the number 38 and an initial guess of 6, then refining the guess by doubling and subtracting remainders. The process is iterative, with each step bringing the approximation closer to the true square root. The tutorial concludes with the square root of 38 being approximated to six point one six, verified by a calculator, showcasing a practical manual technique for square root calculation.
Takeaways
- 📚 The tutorial is about manually calculating the square root of a non-perfect square number, specifically 38.
- 🔍 The presenter starts by identifying that 38 is not a perfect square and therefore requires approximation.
- 📐 The process begins with finding the largest whole number whose square is less than 38, which is 6 (since 6*6=36).
- 📈 A division symbol is used, and the number 38 is divided by 6 to start the approximation process.
- 🔢 A remainder of 2 is calculated after the initial division, leading to the introduction of a decimal point and the process of 'bringing down zeros'.
- 📝 The method involves doubling the current approximation and finding a number to multiply by the last digit to keep the product less than or equal to a certain target (e.g., 200 in the example).
- 📉 Subtraction is used to find the difference between the target and the product, which guides the next step in the approximation.
- 🔄 The process is iterative, with each step refining the approximation by doubling the current number and finding the next digit.
- 📲 The tutorial uses a calculator at the end to verify the manual calculation, showing that the square root of 38 is approximately 6.16.
- 👍 The presenter encourages viewers to give a thumbs up and subscribe if they found the tutorial helpful, highlighting the interactive nature of the content.
Q & A
What is the main topic of the tutorial video?
-The main topic of the tutorial video is to teach viewers how to calculate the square root of a number by hand, specifically the square root of 38 to two decimal places.
Why can't the number 38 be a perfect square?
-The number 38 cannot be a perfect square because there is no whole number that, when multiplied by itself, equals 38.
What is the initial step in the hand calculation process shown in the video?
-The initial step is to write down the number 38 and place a division symbol below it, with the aim of finding a perfect square less than or equal to 38.
What is the first perfect square less than 38 that the tutorial identifies?
-The first perfect square less than 38 identified in the tutorial is 36, which is 6 times 6.
How does the tutorial handle the remainder after finding the initial perfect square?
-The tutorial handles the remainder by placing a dot and then inventing and bringing down two zeros, which is a part of the long division method used to approximate the square root.
What is the purpose of doubling the initial quotient (6) and multiplying it by 2?
-The purpose is to find a three-digit number that, when multiplied by the last digit (2), results in a number less than or equal to 200, which is part of the iterative process to approximate the square root.
What digit is placed in the tenths place of the approximated square root?
-The digit placed in the tenths place of the approximated square root is 1, as derived from the calculation process shown in the video.
How does the tutorial proceed to find the next digit in the square root after finding the tenths place?
-The tutorial proceeds by doubling the number found so far (61) and then finding a whole number to append to it, creating a four-digit number, which is then multiplied by the last digit to find the next digit in the square root.
What is the final approximated square root of 38 given in the video?
-The final approximated square root of 38 given in the video is 6.16.
How does the tutorial confirm the accuracy of the hand-calculated square root?
-The tutorial confirms the accuracy by comparing the hand-calculated square root (6.16) with the result obtained from a calculator, which also shows the square root of 38 to be approximately 6.16.
Outlines
📚 Introduction to Hand Calculation of Square Roots
This paragraph introduces the tutorial on manually calculating square roots. The video begins by addressing the audience and stating the objective: to find the square root of 38 to two decimal places. The presenter explains that since 38 is not a perfect square, an approximation is necessary. The process starts with identifying the largest whole number whose square is less than 38, which is 6, as 6x6=36. The remainder after this division is 2, and the presenter then sets up a template for further approximation, introducing the method of 'bringing down two zeros' and doubling the current estimate to refine the square root approximation.
🔍 Approximating Square Roots by Hand: Detailed Process
The second paragraph delves into the step-by-step process of hand-calculating the square root of 38. The presenter illustrates how to refine the approximation by doubling the current estimate (61 in this case) and setting up a new equation to find the next digit in the square root. The goal is to find a three-digit number that, when multiplied by the last digit of the current estimate, results in a product less than or equal to 200. The presenter identifies '1' as the next digit, leading to an approximation of 6.1. The process is repeated by doubling the new estimate (616) and continuing the search for subsequent digits. The tutorial demonstrates the iterative nature of this manual calculation method, which can be continued to achieve greater precision. The presenter concludes by verifying the manual calculation with a calculator, confirming the approximation of the square root of 38 to be 6.16.
Mindmap
Keywords
💡Square Root
💡Perfect Square
💡Approximation
💡Decimal Places
💡Division Symbol
💡Remainder
💡Multiplication Symbol
💡Less Than or Equal To
💡Tenths Place
💡Double
💡Hand Calculation
Highlights
Introduction to a tutorial on calculating square roots by hand.
Demonstration of finding the square root of 38 to two decimal places.
Explanation that 38 is not a perfect square and requires approximation.
Initial step of setting up the division symbol for the calculation.
Identification of 6 as the largest whole number whose square is less than 38.
Division of 38 by 6 to find the initial quotient and remainder.
Introduction of a unique method involving a dot and bringing down zeros.
Multiplication of the quotient (6) by 2 to find the next digit.
Setting up a template for finding a three-digit number.
Finding the digit '1' as the tenths place of the square root.
Doubling the quotient (61) to continue the approximation process.
Using the less than or equal to symbol to find the next digits.
Multiplication of a four-digit number by a single digit to stay under 79.
Finding the digit '6' as part of the square root approximation.
Continuation of the process with doubling and multiplication.
Final approximation of the square root of 38 to be 6.16.
Verification of the approximation using a calculator.
Conclusion and encouragement to subscribe and engage with the channel.
Transcripts
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