 Any easy method to find square of numbers? A Mathematician With 2-3 Years of Experience Teaching

By Checking the Digit at the Units Place. There will be a pattern.

Easy methods and tricks are not valid all the time, so basic method are always applicable.

Yes, there are. I am trying to explain step by step.Say we want the square of n = 67. First of all, the square of 7 is 49. Write 9 in the answer place and keep 4 for carrying over process.∴n^2 = 9Then, see that 6 and 7 form the number 67. Their product is 42. The rule says you have to double it.... read more

Yes, there are. I am trying to explain step by step.
Say we want the square of n = 67. First of all, the square of 7 is 49. Write 9 in the answer place and keep 4 for carrying over process.
∴n^2 = 9
Then, see that 6 and 7 form the number 67. Their product is 42. The rule says you have to double it. Hence you get double of 42 as 84. Also, you have 4 in your hand for carrying over. Together you get 84+4=88. Write the unit digit eight beside 9 and keep 10s digit 8 for next round carry-over process.
∴ n^2 = 89
Finally, the 10s digit is 6. Square it, and you will get 36. Plus you have 8 in your hand. Together we get 36+8, i.e. 44. Now write it beside 89, and we are done.
∴ 67^2 = 4489.
Try your self: 39^2, 23^2, 52^2.

For squaring three digits or more, there is procedure indeed, but I can't explain them here within short place.

Although I can show you some other special technique for squaring 2 digit numbers of special types.

1. If the number ends with 5:
Let's say we need to square 85. First, write 25 straight forward in answer place.
85^2 = 25

Then, note that after ignoring five we are left with the number 8 in the given number 85. The next number of 8 is 9. The rule says to make the product which is in our present case is 8 x 9, i.e. 72.

Write it down, and we are done.
85^2 = 7225.
Similarly, 95^2 = 9025 because 9 x 10 = 90 and 25 already is written etc.
115^2 = 13225 because 11 x 12 = 132. Etc

2. If the number is near to 100.
Let's say we need to square 93.

The difference between 93 and 100 is 7. The rule says to write down the square of 7 first, which is here 49.
Next, decrease 93 by 7. Which gives 86. Hence the final answer becomes
93^2=8649.
Similarly, 95^2 is 9025 because the difference between 95 and 100 is 5. The square of 5 is 25, and if we decrease 95 by 5, we shall get 90
Together we thus obtain
95^2= 9025.
Notice we have achieved the same already before by using the general squaring technique explained above.

Caution. Suppose we want to square 98. This time doesn't be tempted to write 964. That's not correct. While you are squaring the difference between 100 and the given number, make sure the answer occupies exactly two places only. If not, use 0 to fill up the lattice. Hence 98^2 is not 964 but in 9604.

Similarly, for 88^2, first, write down the square of the difference which is 12^2, i.e. 144. But this time it is a three-digit answer. So keep the last two digits and carry over the excess digit which is 1 in this present case. Now decrease 88 by 12, and we get 76. Added by carried over one we get 77. Hence 88^2 = 7744.

There are more so many special rules. But we can discuss them some other days.

Take care.

Tutor with 2 Years of Experience

Yes there are many methods to find out the square of a number. For 2 digit numnber, you can simply multiply. It is easier only. For 3 digit or more you cancalculate by vadic multiplication method that will be easier.. Thank you.

more than 20 years of experience of teaching Maths to classes 12, 11, 10 and 9 in CBSE schools.

Many shortcuts can be found at Google or You-tube.But please remember that any shortcut will be applicable to a limited number of questions only, falling under a certain category.In general, being good at multiplication and knowing as many tables as possible will only help to be fast and confident.There... read more

Many shortcuts can be found at Google or You-tube.
But please remember that any shortcut will be applicable to a limited number of questions only, falling under a certain category.
In general, being good at multiplication and knowing as many tables as possible will only help to be fast and confident.
There is no shortcut to success, you know!

Yes. Every number is special. you can use algebraic identity to find to the square of any number. First we see about the number end with 9.. Eg:1) 99=100-1 (100-1)^2=100^2-2(100)(1)+1^2 =10000-200+1 =9800+1 =9801. Eg:2) 29=30-1 (30-1)^2=30^2-2(30)(2)+1^2 ... read more

Yes. Every number is special.

you can use algebraic identity to find to the square of any number.

First we see about the number end with 9..

Eg:1) 99=100-1

(100-1)^2=100^2-2(100)(1)+1^2

=10000-200+1

=9800+1

=9801.

Eg:2) 29=30-1

(30-1)^2=30^2-2(30)(2)+1^2

=900-120+1

=780+1

=781

If you practice this directly, start from 2nd step.

Have 25 Years Experience in Teaching

For numbers that end with 5 fix the last 2 digits as 25. And the number to be fixed before, is the product of the 1st digit and it's consecutive number. Example: 45^2= last 2 digits 25. Previous number is the product of 4 and 4+1 , that is, 4×5 =20. So 45^2 =2025

Yes, easily you can find square upto 5 digits square using vedic maths. For example (ab)^2 = a^2|2ab|b^2 (76)^2 = 7^2|2.7.6|6^2 = 49|84|36 = (49+8)|(84+3)|6 = 5776

It Professional With 5+years of Experience in the Field of Software Development

This method uses the identity (a + b) 2 = a 2 + 2ab + b 2 Step 1 : Find 572 Here a = 5 and b =7 Column I Column II Column III a2 2 x a x b b2 52= 25 2 x 5 x 7 =70 72= 49 Step II: Underline the digit of b 2 ( in column III) and add its tens digit, if any, to 2 x a x b (in... read more

This method uses the identity (a + b) 2 = a 2 + 2ab + b 2
Step 1 : Find 572
Here a = 5 and b =7

 Column I Column II Column III a2 2 x a x b b2 52= 25 2 x 5 x 7 =70 72= 49

Step II: Underline the digit of b 2 ( in column III) and add its tens digit, if any, to 2 x a x b (in column III)

 Column I Column II Column III a2 2 x a x b b2 25 70 + 4 = 74 49

Step III: Underline the digit in column II and add the number formed by tens and other digit, if any, to a 2 in column I.

 Column I Column II Column III a2 2 x a x b b2 25 + 7 70 + 4 = 74 49

Step IV: under the number in column I

 Column I Column II Column III a2 2 x a x b b2 32 74 49

Write the underlined digits from the unit digit.
Therefore, 57 2 = 3,249 .

You have to only remember square of number upto 20 , and this will be enough

View 60 more Answers

Related Questions  08 Oct
5 Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Related Lessons

HOW TO FORM CIRCLE,CHORD, RADIUS AND DIAMETER,WHAT IS PIE AND FORMMULLA OF THE PERIMETER OF A CIRCLE.
HOW TO FORM CIRCLE, CHORD, RADIUS AND DIAMETER WHAT IS π FORMULA OF THE PERIMETER OF A CIRCLE. *EVERYTHING INSIDE THE...
A

The site of Photosynthesis:- NEET/AIIMS/JIPMER
The site of Photosynthesis Photosynthesis takes place in Mesophyll cells inside chloroplasts. It is a process which involves chemical reactions in which water and carbon dioxide are converted into energy... Looking to Learn?

Find best Tutors and Coaching Centers near you on UrbanPro.

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you

Best Tutors and Trainers in your Locality Find Now »

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 25 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 6.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more