Squares of numbers ending with 5 | Squares and cubes : Vedic method | UP Math Class 8 | Khan Academy

Khan Academy India - English

12 Feb 202401:44

Summary

TLDRThis educational script explains a method for quickly calculating the square of numbers ending in five. It demonstrates how to break down the number into two parts: the last two digits (which are squared to get 25) and the remaining digits (multiplied by the next consecutive number). Examples include squaring 35 to get 1225, 115 to get 13225, and 85 to get 7225. The technique simplifies the process and is an efficient shortcut for mental math.

Takeaways

🔢 The method described is for squaring numbers that end with the digit 5.
🖋️ The right-hand side of the square is always 25, which comes from squaring the digit 5.
🔗 To find the left-hand side of the square, multiply the first part of the number by its next consecutive number.
🧮 For example, to square 35, multiply 3 by 4, which gives 12, then append 25, resulting in 1225.
📚 The process involves splitting the squaring into two parts: the right-hand side and the left-hand side.
✅ This method works with any number ending in 5, as demonstrated with the example of 115.
🔍 For 115, you multiply 11 by 12 to get 132, and then append 25 to get the full square of 13225.
💡 The right-hand side part (25) remains constant, while the left-hand side comes from the multiplication of the original number's digits.
🧠 The method is applicable to larger numbers, such as squaring 85, where you multiply 8 by 9 and append 25, resulting in 7225.
📝 This approach simplifies the process of squaring numbers ending in 5, making it easier to calculate without traditional long multiplication.

Q & A

What is the method described in the transcript for squaring numbers that end with 5?
-The method described is a technique for squaring numbers that end with 5. It involves separating the number into two parts: the last two digits (which are always 25, as it's the square of 5) and the rest of the digits. The rest of the digits are squared by multiplying the number by the next consecutive integer and then combining the results.
How is the right-hand side part of the square of a number ending with 5 calculated?
-The right-hand side part of the square of a number ending with 5 is always 25, which is the square of 5.
What is the left-hand side part of the square of 35 according to the transcript?
-The left-hand side part of the square of 35 is calculated by multiplying 3 (the number before the last two digits) by 4 (the next consecutive integer), which equals 12.
What is the square of 115 as explained in the transcript?
-The square of 115 is calculated by multiplying 11 by 12 (the next consecutive integer) to get 132, and then appending 25 (the square of 5) on the right. So, 115 squared is 13225.
How is the square of 85 derived in the transcript?
-The square of 85 is derived by multiplying 8 by 9 (the next consecutive integer) to get 72 for the left-hand side part, and appending 25 (the square of 5) on the right. Thus, 85 squared is 7225.
What is the significance of the number 25 in the squaring method described?
-The number 25 is significant because it represents the square of 5, which is the last digit of any number ending with 5. This is a constant part of the square for these numbers.
What is the role of the next consecutive integer in the squaring method?
-The next consecutive integer is used to multiply the digits before the last two digits of the number ending with 5 to form the left-hand side part of the square.
Can this squaring method be applied to numbers that do not end with 5?
-No, the squaring method described in the transcript is specifically for numbers that end with 5. It relies on the fact that the square of 5 is 25.
What is the purpose of adding 1 to the first part of the number before squaring?
-Adding 1 to the first part of the number before squaring is to find the next consecutive integer, which is then used to multiply the original number to form the left-hand side part of the square.
Is there a name for the squaring method discussed in the transcript?
-Yes, the method is referred to as 'Asad' in the transcript.
How does the transcript demonstrate the squaring method with the number 35?
-The transcript demonstrates the squaring method with the number 35 by showing that the square of 35 is 1225, where 12 comes from multiplying 3 by 4 (the next consecutive integer) and appending 25 (the square of 5).

Outlines

00:00

🔢 Squaring Numbers Ending with Five

The paragraph explains a method for quickly calculating the square of numbers that end with the digit five. It uses the example of squaring 35, where the last two digits (25) are the square of five. The remaining digits are obtained by multiplying the tens digit (3) by the next number (4), resulting in 12. This method is applied to other numbers like 115 and 85, where the right-hand side part is always 25, and the left-hand side is calculated by multiplying the tens digit by the next number and appending it to the 25.

Mindmap

Keywords

💡Square of numbers

The term 'square of numbers' refers to the result of multiplying a number by itself. In the context of the video, this concept is central as it explains a method for quickly calculating the square of numbers that end with the digit 5. For instance, the square of 35 is computed by multiplying the tens digit by the next consecutive number and appending the square of 5 (25) to the end.

💡Right-hand side part

This phrase is used to describe the last two digits of the square of a number ending in 5. The video script explains that these digits are always 25, which is the square of 5. This is a key step in the method demonstrated, as it simplifies the process of squaring such numbers by recognizing a consistent pattern.

💡Last two digits

Refers to the digits at the end of a number, which, in the case of numbers ending with 5, are always 25 when squared. The video uses this concept to simplify the calculation process by focusing on these predictable digits, which are easier to compute and remember.

💡Squaring of five

This concept is mentioned in the script to explain the origin of the '25' in the square of numbers ending with 5. The square of 5 is a fundamental part of the method, as it is the constant value that appears on the right-hand side of the squared result for any number ending in 5.

💡Multiplying by its next number

This phrase describes a step in the method for squaring numbers ending with 5. The video demonstrates that to find the left-hand side part of the square, one must multiply the tens digit of the number by the number that follows it in the sequence. For example, in squaring 35, the number 3 is multiplied by 4 (the next number).

💡Filling up

In the context of the video, 'filling up' refers to the process of completing the square of a number by combining the calculated left-hand side part with the predetermined right-hand side part (25). This term is used to describe the final step in the method, where the two parts are concatenated to form the complete square.

💡Method

The 'method' discussed in the video is a specific technique for calculating the square of numbers ending with 5. It is a systematic approach that involves recognizing patterns and applying a set of rules to simplify the calculation. The method is practical and efficient, making it easier to remember and use.

💡Reinforce

The term 'reinforce' is used in the script to emphasize the importance of practicing and repeating the method to solidify understanding. The video provides additional examples to reinforce the learning, ensuring that viewers grasp the technique thoroughly.

💡115 square

This is an example used in the video to illustrate the method. The script explains how to calculate the square of 115 by following the steps outlined in the method. The result, 13225, is derived by multiplying 11 by 12 and appending 25, demonstrating the practical application of the method.

💡85 square

Similar to '115 square,' this is another example provided in the script to demonstrate the method. The square of 85 is calculated by multiplying 8 by 9 and appending 25, resulting in 7225. This example further illustrates the method's applicability to numbers ending in 5.

Highlights

Method for squaring numbers ending with five explained.

Squaring 35 example provided, demonstrating the process.

The last two digits of a number ending in five always square to 25.

The left-hand side part of the square is calculated by multiplying the number by the next number.

For 35, the left-hand side part is 4 * 3 which equals 12.

The square of 35 is 1225, combining both parts.

The method is referred to as Asad's method.

Squaring 115 example, with right-hand side part being 25.

Left-hand side part for 115 is calculated by multiplying 11 by 12.

The square of 115 is 13225, combining left and right-hand side parts.

Squaring 85 example, with right-hand side part being 25.

Left-hand side part for 85 is calculated by multiplying 8 by 9.

The square of 85 is 7225, combining both parts.

The process is a quick method for squaring numbers ending in five.

The method involves breaking down the number into parts for easier calculation.

The method is particularly useful for mental math and quick calculations.

The transcript provides a step-by-step guide to the method.

The method can be applied to any number ending with five.