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

Summary

This 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).