Square Root of 26

The square root of 26 can be determined by the prime factorisation and long division method. As 26 is not a perfect square number, we get an irrational root. A perfect square number is a number that can be written as a square of an integer. The square root of a number is just the opposite of squaring. In radical form, the square root of 26 is denoted as √26, and in the exponential form, it is written as (26)^½ or (26)^0.5. In this article, we shall learn how to find the square root of 26.

What Is the Square Root of 26?

The square root of 26 is a number whose square gives the result 26. Now, 26 is not a perfect square number because we cannot find any integer which could be multiplied twice to get 26.

Let q be any real number, such that 26 = q × q = q².

Thus, we find an approximate value of the square root of 26, as it is an irrational number.

The square root of 26 can also be determined by finding the roots of the quadratic equation

q² – 26 = 0

⇒ q² = 26

Taking square roots on both sides, we get,

⇒ q = √26

⇒ q = ± 5.099 (approx.)

How to Find the Square Root of 26?

Let us find the square root of 26 using the prime factorisation and long division method. The repeated subtraction method will not give an accurate value as 26 is not a perfect square, and its square root is an irrational number.

Repeated Subtraction Method

To find the square root by the repeated subtraction method, we have to successively subtract odd consecutive numbers from the given number. Continue subtracting odd numbers till we get the difference zero. If the difference is zero, the given number is a perfect square; otherwise, it is not a perfect square.

Clearly, 26 is not a perfect square number. But we could easily tell that the square root of 26 lies between 5 and 6.

Prime Factorisation Method

To find the square root of 26 by the prime factorisation method, we first prime factorise 26 and then make pairs of two to get the square root.

Prime factorisation of 26 = 2 × 13

Square root of 26 = √[2 × 13] ≈ 5.099

Long Division Method

To find the square root of 26 by the long division method, we shall write 26 as the dividend and pair its digits from right to left. Now, we shall calculate the square root as follows:

Therefore, the square root of 26 by the division method is 5.099 (up to 3 decimal places). This division could go infinitely without repeating any pattern, which proves root 26 is an irrational number.

To learn how to find the square root of any number by the long division method, click here.

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Solved Examples on Square Root of 26

Example 1:

Find the diameter of the circle whose area is 26𝜋 m².

Solution:

Let r be the radius of the circle.

The area of the circle = 𝜋r² = 26𝜋 m²

⇒ r² = 26 (taking square root on both sides)

⇒ r = √26

⇒ r = 5.099 m (taking the positive root as length cannot be negative)

∴ the diameter of the circle = 2 × 5.099 = 10.198 m (approx.).

Example 2:

Find the length of the base of a triangle whose area is 2.6 m² and the height is one-fifth of its base.

Solution:

Let ‘b’ be the base of the triangle.

Height of the triangle = b/5

Area of the triangle = ½ × b × b/5 = 2.6 m²

⇒ 1/10 × b² = 2.6

⇒ b² = 26 (taking square root on both the sides)

⇒ b = √26 = 5.099 m

∴ the length of the base of the triangle is 5.099 m.

Example 3:

What is the smallest number that should be added with 26 to make it a perfect square number? Also, find the square root of that number obtained.

Solution:

Clearly, 26 < 36 = 6²

Therefore, we must add 10 with 26 to make it a perfect square number.

26 + 10 = 36 is the required perfect square.

√36 = ± 6