Worksheet Solutions: Squares | Improve Your Calculations: Vedic Maths (English) - Class 6 PDF Download

Q1: Find the square of the number 95 using Vedic Mathematics.
(a) 9025
(b) 9125
(c) 8025
(d) 8125

Ans: (a)
Explanation: Given:
We have to find the square of the number 95 using Vedic Mathematics.
Now, before we proceed we should know what the method is to find the squares of the number ending with 5 in Vedic Mathematics. We can understand the method with the help of one example. Suppose we have to find out the square of 85. Then, follow the following steps:
1. Multiply 5 by 5 and put 25 on the right-hand side.
2. Add one to the left digit i.e., 8 + 1 = 9
3. Multiply 9 by 8 to get 72 and write it on the left-hand side.
4. Our answer is 7225.
Now, for better understanding, we take one more example. Suppose we have to find the square of 105. Then, follow the following steps:
1. Multiply 5 by 5 and put 25 on the right-hand side.
2. Add one to the left digit i.e., 10 + 1 = 11
3. Multiply 11 by 10 to get 110 and write it on the left-hand side.
4. Our answer is 11025.
Now, we can find the square of 95 by the following steps:
1. Multiply 5 by 5 and put 25 on the right-hand side.
2. Add one to the left digit i.e., 9 + 1 = 10
3. Multiply 10 by 9 to get 90 and write it on the left-hand side.
4. Our answer is 9025.
Thus, the square of 95 will be 9025.
Hence, (a) is the correct option.

Q2: Find the square of the number using Vedic Mathematics.
(132)² 

Ans:
Steps:
1. Square the digit at the unit's place, 2² 
= 4. Write 4 at the unit's place of the answer.
2. Take the number except the unit's place digit, 13, multiply it to the unit's place digit, 13 × 2 = 26 and multiply it by 2, 26 × 2 = 52
3. Square the number except the unit's place digit and write in the leftmost part, 13²
= 169.
4. Keeping in mind that the second and third places should only contain one digit, carry forward as required. 169/52/4 = 174/2/4
5. Append the numbers. 17424 is the answer.

Q3: Squaring of number ending with 5.
155

Ans: 

Q4: Squaring of numbers less than 50 and numbers not ending with 5.
28

Ans:

Q5: Squaring of number near to their base 10, 100, 1000, and so on.
986

Ans:

Q6: Squaring of a number near to their sub-base.
(i) 306

Ans:

(ii) 480

Ans:

Q7: Squaring of numbers less than 50 and numbers not ending with 5.
74

Ans: