All questions of Squares and Square Roots for Class 6 Exam

Because if we add the number 5 five times we will get the approximate number 25

Step-by-Step Explanation:

Given Number: 148

1. Decomposition:
- Write the number as 100a + 10b + c
- For 148, a = 1, b = 4, c = 8

2. Duplex Calculation:
- Add the last digit (c) to the square of the first digit (a^2) and write the result in the unit's place.
- For 148, 8 + 1^2 = 9 (Write 9 in the unit's place)
- Double the product of the first and last digit (2 * a * c) and add it to the product of the first and second digit (2 * a * b) and write the result in the ten's place.
- For 148, 2 * 1 * 8 + 2 * 1 * 4 = 16 + 8 = 24 (Write 4 in the ten's place and carry over 2)
- Add the carried-over number (if any) to the square of the middle digit (b^2) and write the result in the hundred's place.
- For 148, 2 + 4^2 = 18 (Write 8 in the hundred's place)
- If there is a carry in the hundred's place, carry it over to the thousand's place.

3. Square of the Given Number:
- Combine the results from the duplex calculation to get the square of the given number.
- For 148, the square is 21904.
Therefore, the square of 148 using the duplex method is 21904.

Solution:

To find the square root of a four-digit perfect square number, we need to determine the two-digit number whose square is equal to the given four-digit number.

Given number: 1024

Step 1: We start by finding the square root of the first two digits of the given number, which is 10. The square root of 10 is approximately 3.16.

Step 2: Next, we need to determine the correct digit for the units place. To do this, we consider the remaining two digits of the number, which is 24.

Step 3: We check the square of the number obtained in step 1 (3), by multiplying it with the next consecutive number. In this case, 3 * 4 = 12.

Step 4: We compare the value obtained in step 3 (12) with the remaining two digits of the given number (24). If the value in step 3 is less than the remaining two digits, we increment the digit of the units place by 1.

Step 5: We repeat step 3 and step 4 until the value obtained in step 3 is greater than or equal to the remaining two digits of the given number.

Step 6: From the above steps, we find that the square root of the given number 1024 is 32.

Therefore, the correct answer is option 'B' (32).

Explanation:

Duplex Method:
The duplex method is a technique used to find the square of a number quickly. It involves breaking down the number into tens and units and then calculating the square.

Given Number: 26
To find the square of 26 using the duplex method, follow these steps:

Step 1: Break down the number into tens and units.
26 = 20 + 6

Step 2: Calculate the square of the tens and units separately.
20^2 = 400
6^2 = 36

Step 3: Multiply the tens by the units and double the result.
2 * 20 * 6 = 240

Step 4: Add the results from steps 2 and 3 to get the square of the given number.
400 + 36 + 240 = 676
Therefore, the square of 26 using the duplex method is 676.

Correct Answer: 676 (Option B)

Explanation:

Duplex Method:
The duplex method is a technique used to find the square of numbers quickly and efficiently. It involves breaking down the number into two parts and performing calculations based on those parts.

Given Number: 88

Calculations:
- Step 1: Take the first part of the number, which is 88, and find the square of this part.
- 88^2 = 7744
- Step 2: Take the second part of the number, which is 8, and find the square of this part.
- 8^2 = 64
- Step 3: Multiply the first part by the second part and double the result.
- 88 * 8 * 2 = 1408
- Step 4: Combine the results from Step 1, Step 2, and Step 3 to get the final answer.
- Final Answer = 7744 | 1408 | 64 = 6944
Therefore, the square of 88 using the duplex method is 6944.