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

Q1: Square root of perfect square number.
√3969

Ans:

Q2: Square root of imperfect square number.
√2

Ans:

Q3: Find the Square root.
√6889

Ans:
There are two groups of figures, '68' and '89'. So we expect 2-digit answer.
Now see since 68 is greater than 64(8²) and less than 81(9²), the first figure must be 8.
So, 6889 is between 6400 and 8100, that means, between 80² and 90².
Now look at the last figure of 6889, which is 9.
Squaring of numbers 3 and 7 ends with 9.
So, either the answer is 83 or 87.
There are two easy ways of deciding. One is to use the digit sums.
If 872 = 6889
Then converting to digit sums
(L.H.S. is 8 + 7 = 15 -> 1+5 -> 6 and R.H.S. is 6 + 8 + 8 + 9 -> 31 -> 3 + 1 -> 4)
We get 6² -> 4, which is not correct.
But 832 = 6889 becomes 22 -> 4, so the answer must be 83.
The other method is to recall that since 85² = 7225 and 6889 is below this. 6889 must be below 85. So it must be 83.

Q4: Find the Square root.
√5776

Ans: The first 2-digit(i.e. 57) at the beginning is between 49 and 64, so the first figure must be 7.
The last digit (i.e. 6) at the end tells us the square root ends in 4 or 6.
So the answer is 74 or 76.
74² = 5776 becomes 2² -> 7 which is not true in terms of digit sums, so 74 is not the answer.
76² = 5776 becomes 4² > 16 -> 7, which is true, so 76 is the answer.
Alternatively, to choose between 74 and 76 we note that 75² = 5625 and 5776 is greater than this so the square root must be greater than 75. So it must be 76.

Q5: Find the Square root.
√729 

Ans: 
1. Splits the number keeping last 2 digits aside i.e.
          7 ǀ 29
2. Check the square digit of number 9 & its unit Square digit is 3& 7
3. Next check Square 7 it lies between 2 & 3 Square (2² = 4, 3² = 9)
4. Choose the smaller number i.e.2
5. Now there is two possibilities for answer i.e. 23 or 27.
6. The smaller number is 2, consider the next number of 2 is 3 multiply those two number 2 × 3 = 6 ,6 is smaller as we compare to given digit i.e. 7 (6 ˂ 7).
7. We have to consider the greater number i.e. 27 so the final answer will be 27.
√729 = 27

Q6: Find the Square root.
√1024

Ans: 
1. Splits the number keeping last 2 digits aside i.e.
    10 ǀ 24
2. Check the square digit of number 4 & its unit Square digit is 2& 8
3. Next check Square 10 it lies between 3 & 4 Square (32 = 9, 42 = 16)
4. Choose the smaller number i.e. 3
5. Now there is two possibilities for answer i.e. 32 or 38
6. The smaller number is 3, consider the next number of 3 is 4 multiply these twos’ number 3 × 4 = 12 , 12 is greater as we compare to given digit i.e.10 (12 > 7)
7. We have to consider the smaller number i.e.32 so the final answer will be 32.
√1024 = 32

Q7: Find the Square root.
√76176

Ans: 
1. Splits the number keeping last 2 digits aside i.e.
       7 61 ǀ  76
2. Check the square digit of number 6 & its unit Square digit is 4& 6
3. Next check Square 716 it lies between 27&28 Square (27² = 729, 28² = 784)
4. Choose the smaller number i.e.27
5. Now there is two possibilities for answer i.e. 274 or 276.
6. The smaller number is 27, consider the next number of 27 is 28, multiply those two number 27 × 28 = 756, is smaller as we compare to given digit i.e.761 (756 ˂ 761).
7. We have to consider the greater number i.e.276 so the final answer will be 276
√76176 = 276