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Square root of 26

The square root of 26 is a number which when multiplied by itself, results in the number 26. Without saying more, let us see how to calculate the value of the square root of 26 and see some problems to help us understand this topic.

Square Root of 26: √26 = 5.09901951...
Square of 26: 26² = 676

1.	What is the Square Root of 26?
2.	Is Square Root of 26 Rational or Irrational?
3.	How to Find the Square Root of 26?
4.	FAQs on Square Root of 26

What is the Square Root of 26?

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 26 can be written in multiple ways

Radical form: √26
Decimal form: 5.09902
Exponent form: (26)^1/2

Is Square Root of 26 Rational or Irrational?

26 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
Also, its square root cannot be expressed as a fraction of the form p/q which confirms to us that the square root of 26 is an irrational number.

How to Find the Square Root of 26?

There are multiple ways to find the square root of 26-

Long Division Method
Estimation and Approximation

One can find out more about these methods by clicking here

Long Division Method

The square root of 26 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits 26 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 26. The number 5 fits here as 5 squared gives 25. Dividing 26 by 5 with quotient of 5, we get the remainder as 1.
Step 3: Drag a pair of 0’s down and fill it next to 1 to make the dividend 100.
Step 4: Double the divisor 5, and enter 10 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 16X and X results in a value less than or equal to 100. This will be 0. Divide and write the remainder.
Step 5: Repeat this process to get the decimal places you want.

Square Root of 26

Therefore, the square root of 26 = 5.09

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

Step 1: Find a perfect square that is smaller than and bigger than 26. In this case, 4 and 6 will work as their squares are 16 and 36.
Step 2: Writing in terms of inequality: 4 < √26 < 6 = 16 < 26 < 36
Step 3: Multiply by 10 and write in terms of square roots: √1600 < √2600 < √3600
Step 4: Move closer to inequality: √2500 < √2600 < √2601 = 50 < 10√26 < 51 = 5 < √26 < 5.1
Step 5: Taking the average of upper and lower limits we get, (5 + 5.1)/2 = 5.05

Therefore, we can estimate the square root of 26 ≅ 5.05

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Important Notes

There exists a positive and negative root of 26, 5.9902 and -5.9902.
The square root of 26 is an irrational number that is non-terminating.

Challenging Questions

What is the square root of 26 up to 10 decimal places(Use Long Division)?
Find the square root of the following numbers:
- 2600
- 0.26

Example 1: John wants to calculate the side length of his square garden in his home. It has an area of 26 square feet.

Solution:

To find the side of the land, we will have to find the square root of 26. The square root is √26 = 5.099.
Hence, the side length of the garden is approximately 5 feet.
Example 2: Joel was asked to solve an equation x² - 676 = 0. Help him find all values of x

Solution:

x² - 676 = 0
x² = 676.
Taking the square root on both sides, we get
x = ±26

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FAQs on Square Root of 26

What is the prime factorization of 26?

The prime factorization of 26 is 2 × 13.

Is 26 a perfect square root?

26 is not a perfect square. 26 is a natural number, but since there is no other natural number that can be squared to result in the number 26, it is NOT a perfect square.

What is the decimal value of the square root of 26?

The decimal value of the square root of 26 is 5.099.

Is the square root of 26 a rational number?

No, the square root of 26 is not a rational number since the square root of 26 is non-terminating and cannot be represented in the form of p/q.

Can we find the square root of 26 by the repeated subtraction method?

No, we can’t find the square root of 26 by repeated subtraction method as it can be used only for perfect squares. 26 is not a perfect square.

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