Square Root of 529

Square root of 529 is 23 and is represented as √529 = 23. 

Consider the numbers 25, 36, 49… These are obtained by multiplying a number with itself. i,e 25 = 5 × 5, 36 = 6 × 6 and 49 = 7 × 7 and so on. The numbers 25, 36, 49 are termed as perfect square numbers and 5, 6, 7 are termed as square roots for 25, 36 and 49 respectively. If the number 529 is a perfect square, then there will be an integer “y” such that “y ×y” = 529, where “y” will be the square root of 529. Let us determine the value of “y” using different methods that are detailed below.

Note the Following:

The Square root of 529 = √529 where √ = radical, and 529 is the radicand.

Exponential Form of Square root of 529 = 5291/2

Solution for √529 = 23

Square root of 529 is Irrational = Fasle

For the detailed explanation on square roots can be obtained from Squares and Square roots.

What is the Square root of 529?

The square root of 529 is 23. In other words, the square of 23 is 529. i.e ±23 × ±23 is 529. 

√529 = 23

How to Find the Square root of 529?

There are three methods to find the Square root of 529:

  • Prime Factorisation method
  • Long Division method
  • Repeated Subtraction method

Square root of 529 by Prime Factorisation Method

In the Prime Factorisation method, the following steps are followed;

  1. Divide 529 by prime divisors. Only 23 divided 529.
  2. Since 23 x 23 is 529, 23 is the square root. 

Division for 529 is;

23

529

23

23

×

1

529 = 23 × 23 

529 = (23 × 23)

√529 = √(23 × 23)

√529 = 23

Therefore the square root of 529 = 23.

Square root of 529 by Long Division Method

In the long division method, the given numbers are paired in groups, starting from the right side. Let us understand the long division method, in detailed steps;

Step 1:  Grouping the given number into pairs

Given number is 529, grouping it as 2 and 56.

Step 2: Consider the first number.

Let us find a square number that divides the first number

i.e 1 × 1 = 1 

2 × 2 = 4 

3 × 3 = 9.

Step 3: Continue the division using the next number 29. The first number to be used as the next divisor (Divisor of first division multiplied by quotient of first division)

Square root of 529

 

The Division completes with zero remainder. Hence the quotient is the square root, which is 23 for 529. 

Square root of 529 by Repeated Subtraction Method.

In the repeated subtraction method, the number 529 is decreased repeatedly by odd numbers. This results in

  1. Difference = zero; Then 529 is a perfect square with the perfect square root.
  2. Difference = negative; Then 529 is not a perfect square and it has an irrational root. 

For the given number 529, steps for repeated subtraction are

Step 1

529

1

=

528

Step 2

528

3

=

525

Step 3

525

5

=

520

Step 4

520

7

=

513

Step 5

513

9

=

504

Step 6

504

11

=

493

Step 7

493

13

=

480

Step 8

480

15

=

465

Step 9

465

17

=

448

Step 10

448

19

=

429

Step 11

429

21

=

408

Step 12

408

23

=

385

Step 13

385

25

=

360

Step 14

360

27

=

333

Step 15

333

29

=

304

Step 16

304

31

=

273

Step 17

273

33

=

240

Step 18

240

35

=

205

Step 19

205

37

=

168

Step 20

168

39

=

129

Step 21

129

41

=

88

Step 22

88

43

=

45

Step 23

45

45

=

0

Step 23 leads to the difference zero, which implies that 529 is a perfect square number and hence 23 is its root. 

Video Lessons

Visualising square roots

Finding Square roots

Related Articles

Solved Examples

1. Find the square root of 529 by pairing factors.

The pairs of 529 are (1, 529) and (23, 23)

Therefore the square root of 529 is 23 using pairing factors 23 and 23. 

2. What is the square of 23?

The square of 23 is nothing but 23 times 23 and that is 529.

Frequently Asked Questions on Square root of 529

Q1

What is the Square root of 529?

The Square root of 529 is 23.
Q2

Are the square of 23 and square root of 529 the same?

No. The square of 23 is 529 whereas the square root of 529 is 23. They are not the same.
Q3

What are the factors of 529?

The factors of 529 are 1, 23 and 529.
Q4

Square root of 529 is irrational. True or False?

False. Square root of 529 is 23. Hence it is not an irrational number.
Q5

529 is a perfect square number. True or False?

True. 529 is a perfect square number as 23 square is 529.

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