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Square Root of 29

Before we begin, let's understand the meaning of the square root. The symbol square root is written as √ and is an integral part of mathematics. Once you understand the basics of finding the square root of a number, you can solve any square root-related problem. In this short lesson, we will learn about the square root of 29. We will do so using methods like prime factorization and division, and along with it, also find out the square root of 29.

Square Root of 29: √29 = 5.385
Square of 29: 29² = 841

1.	What Is the Square Root of 29?
2.	Important Notes on Square Root of 29
3.	How to Find the Square Root of 29?
4.	Important Notes on Square Root of 29
5.	Thinking Out of the Box!
6.	FAQs on Square Root of 29

What Is the Square Root of 29?

We know that addition has an inverse operation as subtraction and multiplication has an inverse operation as division. Similarly, finding the square root is an inverse operation of squaring. The square root of 29 is the number that gets multiplied to itself to give the number 29. So, we have to think of a number whose square is 29. We can see that, there does not exist any integer whose square is 29. The square root of a number is the number that gets multiplied to itself to give the original number. The square root of 29 is 5.38516480713.

Is the Square Root of 29 Rational or Irrational?

It is not possible to break 29 into two such factors which, on squaring, give 29. It can be approximately written as a square of 5.385, which is a non-recurring and non-terminating decimal number. This shows that it is not a perfect square, which also proves that the square root of 29 is an irrational number. Do you think the square root of 29 and the square root of 5 have anything in common? Yes, there is, both are prime numbers and are not perfect squares. So √29 is an irrational number.

How to Find the Square Root of 29?

We can find the square root of 29 using the following steps:

Step 1: Check whether the number is a perfect square or not. In this case, 29 is not a perfect square as it cannot be broken down into a product of two same numbers.
Step 2: Once the number is checked, the following process needs to be followed:

If the number is a perfect square, it can be written as √x²= x
If it is not a perfect square, the square root is found using the long division method. It can also be written in its simplified radical form.

Since 29 is not a perfect square, we find its square root using the long division method. The simplified radical form of the square root of 29 is given below.

Simplified radical form of the square root of 29

29 can be written as a product 1 and 29.
√29 = √(1 × 29)
29 is not a perfect square, hence, it remains within roots. The simplified radical form of the square root of 29 is √29.

Square Root of 29 By Long Division

Let us understand the process of finding the square root of 29 by long division.

Step 1: Pair the digits of the number starting from the right end, by placing a bar over them.
Step 2: Now, we find a number such that its square gives a product that is less than or equal to this pair. The square of 5 is 25, which is less than 29. On subtracting 25 from 29, we get 4.
Step 3: Now, we double the quotient and place it as the next divisor with a blank on its right. The double of 5 gives 10 and a blank is placed next to it. This blank needs to be filled by a number which will also become the next digit in the quotient. It should be filled with the largest possible digit, such that when the new divisor is multiplied with the new quotient, the product is less than or equal to the dividend.
Step 4: Repeating the above steps, the quotient 53 is doubled, which gives 106, and a pair of 0s is added to the dividend.
Step 5: The same steps are repeated and the digit which is written in the blank is 8. The product of 1068 and 8 gives 8544. After subtracting 8544 from 9100, we get 556 with a new pair of 0s.Finally, the square root of 29 is calculated to be 5.385 as shown below:

square root of 29

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Important Notes:

29 is not a perfect square, hence, its square root is an irrational number. This concludes that the square root of any number "n", which is not a perfect square, will always be an irrational number.

Think Tank:

Can you find the square root of 29 using the long division method up to 5 decimal places?
Express the square root of 290 in its simplified radical form.

Square Root of 29 Solved Examples

Example 1: The square root of 29 lies between two consecutive numbers. Can you help Darcy find those 2 numbers?

Solution

Darcy knows that 29 is not a perfect square. However, the two perfect squares nearest to 29 are 25 and 36.
The square root of 25 is 5.
The square root of 36 is 6.
Hence, the square root of 29 lies between 5 and 6.
Example 2: Help Lucas prove that half of the square root of 58 is not the same as the square root of 29.

Solution

Lucas knows 58 can be expressed as √58 = √(2 × 29)

Half of the square root of 58 is:
√58/2 = √(2 × 29)/2 = √29/2
The square root of 29 is √29. This proves the statement that half of the square root of 58 is not the same as the square root of 29.

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FAQs On Square Root of 29

What is the square root of 29?

The square root of 29 is 5.38516480713

What is the square of 29?

The square of 29 is 841.

How do you find the square root of 29?

We can find the square root of 29 by using the prime factorization and long division.

Is the square root of 29 an irrational number?

Yes, the square root of 29 is an irrational number.

What is the square root of 29 in simplified form?

The square root of 29 in simplified form is √29.

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