Square Root of 44

Let us find the square root of 44 using the prime factorisation and long division method. A perfect square number is a number that can be written as a square of a particular number. For 44, we cannot find any integer whose square is 44. The square root of a number is just the opposite of squaring. If a² = b, then b^1/2 = a. In radical form, the square root of 44 is written as √44, and in the exponential form, it is written as (44)^½. In this article, we shall learn how to find the square root of 44.

Learn more about square and square roots.

What Is the Square Root of 44?

The square root of 44 is a number whose square gives the result 44. Now, 44 is not a perfect square number because we cannot find any integer which could be multiplied twice to get 44. Thus, we find an approximate value of the square root of 44, as it is an irrational number.

The square root of 44 is also the root of the quadratic equation x² – 44 = 0.

x² – 44 = 0

⇒ x² = 44

Taking the square root on both sides, we get,

⇒ x = √44

⇒ x = ±2√11

How to Find the Square Root of 44?

Let us find the square root of 44 using the prime factorisation and long division method. The repeated subtraction method will not work as 44 is not a perfect square, and its square root is an irrational number.

Prime Factorisation Method

To find the square root of 44 by the prime factorisation method, we first prime factorise 44 and then make pairs of two to get the square root.

Prime factorisation of 44 = 2 × 2 × 11

Square root of 44 = √[2 × 2 × 11] = 2 × √11 = 2√11

Long Division Method

To find the square root of 44 by the long division method, we shall write 44 as a dividend and pair its digits from right to left. To get the square root in decimal, we place a decimal after 44 and then two pairs of zeros. Now, we have to calculate the square root of 44 as follows:

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

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Solved Examples on Square Root of 44

Example 1:

Find the perimeter of the circle whose area is 44𝜋 m².

Solution:

Let r be the radius of the circle.

The area of the circle = 𝜋r² = 44𝜋 m²

⇒ r² = 44 (taking square root on both sides)

⇒ r = √44

⇒ r = 2√11 m (taking the positive root as length cannot be negative)

∴ the perimeter of the circle = 2𝜋r = 2 × 𝜋 × 2√11 = 4𝜋√11 m

Example 2:

Find the roots of the equation (x² – 2x)/4 = (22 – x)/2.

Solution:

We have (x² – 2x)/4 = (22 – x)/2

⇒ 2x² – 4x = 88 – 4x

⇒ 2x² – 88 = 0

⇒ x² – 44 = 0

⇒ x = √44 = ±2√11

∴ x = 2√11 and –2√11

Example 3:

What is the smallest number that should be multiplied by 44 to make it a perfect square number? Also, find the square root of the number obtained.

Solution:

Now, the square root of 44 = 2√11.

Then 44 × 11 = 484 will be the perfect square number. Thus, 11 is the smallest number that should be multiplied.

√484 = 22