Squares of numbers ending with 5 | Squares and cubes : Vedic method | UP Math Class 8 | Khan Academy
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
🔢 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
💡Right-hand side part
💡Last two digits
💡Squaring of five
💡Multiplying by its next number
💡Filling up
💡Method
💡Reinforce
💡115 square
💡85 square
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.
Transcripts
let us see how the squares of numbers
ending with five are done so for example
if we want to square 35 there are two
parts of the square one is the right
hand side part which are the last two
digits and these last two digits are
always 2 and five which is basically the
square of five so this 25 comes from the
squaring of five and rest of the earlier
digits or the square of 35 come from
multiplying this number by its next
number so we add 1 to three and then we
multiply that with the original number
and that gives us 4 * 3 which is 12 and
I can just fill it up and so this is the
square of 35 so we could just say 35
square is
1225 this method is known
Asad let's just reinforce what we just
studied let's take one more example so
if we wanted to square
115 so the right hand side part is going
to be 25 and then what we will do is
that we will multiply 11 with 12 because
12 is the next number for 11 and the
multiplication of 11 and 12 is 132 and
we just put 132 on the left hand side of
25 and that is the square of 115 so
basically 115 square is
13,22 let us Square 85 square of 5 is 25
that is being put on the right then we
do 8 * 9 which is 72 so this is the left
hand side part this is the right hand
side part we just combine those and that
is the square of 85
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