Square Root Of Perfect Square

Are you searching to learn Square Root of a Perfect Square by Using the Long Sectionalization Method? Then, you can become the procedure to detect a Foursquare Root of a Perfect Square with the aid of a Long Segmentation Method hither. Nosotros have included unlike types of bug, solutions, and as well their caption. Therefore, without any filibuster, you can brainstorm your do and get a grip on the complete concept.

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How to observe Square Root of a Perfect Square Number using Long Division Method?

Bank check the beneath steps to learn the procedure for finding the Foursquare Root of a Number using the Long Division method.

Group the digits in pairs using a flow that starts with the digit in the units identify. Each pair and the remaining digit (if any).
Set the largest number whose foursquare is equal to or just less than the first period. Then, you have to take this number equally the divisor and as well as the caliber.
Do subtract the production of the divisor and the quotient from the showtime menses.
Then, write the next period to the right of the remainder and consider it as a new dividend.
Dissever the new dividend until the digit is equal to or but less than the new dividend.
Repeat the above steps till all the periods have been taken up. At present, the quotient so obtained is the required square root of the given number.

Square Root of a Perfect Foursquare Number using Long Division with Examples

1. Find the foursquare root of 784 by the long-division method?

Solution:
The given number is 784.
To observe the square root of a perfect square by the long sectionalisation method, we accept to follow the below procedure.
784 = 2 x 2 x 2 10 2 10 seven x 7
Group the factors into the pairs of equal factors.
(2 × 2) × (2 × 2) × (7 × 7)
Have one number from each grouping and multiply them to find the number whose square is 784.
ii × 2 × 7 = 28.

The square root of 784 is 28.

2. Evaluate √5329 using the long-division method?

Solution:
The given number is √5329.
To observe the foursquare root of a perfect square by the long division method, nosotros have to follow the beneath process.
√5329 = 73 x 73
Grouping the factors into the pairs of equal factors.
(73 × 73)
Take one number from each group and multiply them to find the number whose square is 5329.
73.

The square root of 5329 is 73.

3. Evaluate √16384?

Solution:
The given number is √16384.
To observe the square root of a perfect square by the long division method, we take to follow the beneath procedure.
√16384 = 2 x 2 x 2 x 2 x 2 ten 2 x 2 x two x two ten ii 10 two ten 2 10 two ten two
Group the factors into the pairs of equal factors.
(two × 2) x (two × 2) x (two × 2) x (2 × ii) 10 (ii × 2) ten (2 × 2) 10 (ii × 2)
Have one number from each group and multiply them to find the number whose square is 16384.
ii x two × 2 x 2 × 2 x 2 × 2 = 128.

The square root of 16384 is 128.

4. Evaluate √10609?

Solution:
The given number is √10609.
To find the square root of a perfect foursquare by the long division method, we have to follow the below process.
√10609 = 103 x 103
Grouping the factors into the pairs of equal factors.
(103 x 103)
Take one number from each group and multiply them to find the number whose foursquare is 10609.
103

The square root of 10609 is 103.

5. Evaluate √66049?

Solution:
The given number is √66049.
To observe the square root of a perfect square by the long sectionalisation method, we have to follow the below procedure.
√66049 = 257 10 257
Grouping the factors into the pairs of equal factors.
(257 x 257)
Take one number from each grouping and multiply them to find the number whose foursquare is 66049.
257

The square root of 66049 is 257.

6. Find the cost of erecting a contend effectually a square field whose area is 4 hectares if fencing costs $ 3.l per meter?

Solution:
Area of the foursquare field = (four × 1 0000) thousand² = 40000 m²
Length of each side of the field = √40000 m = 200 m.
Perimeter of the field = (4 × 200) m = 800 m.
Cost of fencing = $(800 × 7/2) = $2800.

seven. Observe the least number that must exist added to 6412 to make it a perfect square?

Solution:
Given the number is 6412,
To detect the square root of a perfect square by the long division method, we accept to find the factors of 6412.
6412 = (80 × 80)
Grouping the factors into the pairs of equal factors.
(80 × fourscore)
Nosotros discover here that (80)² < 6412 < (81)²
The required number to be added = (81)² – 6412
= 6561 – 6412
= 149

viii. What least number must be subtracted from 7250 to go a perfect square? Likewise, find the foursquare root of this perfect square?

Solution:
Given the number is 7250,
To find the foursquare root of a perfect foursquare by the long partition method, we have to notice the factors of 7250.
7250 = (85 × 85)
Grouping the factors into the pairs of equal factors.
(85 × 85)
Then, the least number to be subtracted from 7250 is 25.
Required perfect square number = (7250 – 25) = 7225
And, √7225 = 85.

9. Notice the greatest number of iv digits which is a perfect square?

Solution:
The greatest number of 4 digits is 9999.
The foursquare root of 9999 is
To find the square root of a perfect square past the long sectionalization method, we have to detect the factors of 9999.
9999 = (99 × 99)
Grouping the factors into the pairs of equal factors.
(99 × 99)
This shows that (99)² is less than 9999 by 198.
So, the least number to be subtracted is 198.
Hence, the required number is (9999 – 198) = 9801.