Square Root of 1936

The square root of 1936 is a number whose square is 1936. A perfect square is a number that can be expressed as a square of any integer; 1936 is a perfect square number as (± 44)² = 1936. The square of 1936 in radical form is written as √1936, and in the exponential form, it is written as (1936)^½. In this article, we shall learn how to calculate the square root of 1936 using the prime factorisation and long division method.

Learn more about square and square roots.

What Is the Square Root of 1936?

The square root of 1936 is a number that, when multiplied twice by itself, gives the answer 1936. The number 1936 is a perfect square, as we can find integers 44 and –44, whose square is 1936.

Now, we have the quadratic equation x² – 1936 = 0; on solving the equation,

x² – 1936 = 0

⇒ x² = 1936

Taking square root on both sides, we get,

⇒ x = √1936

⇒ x = ± 44

Thus, the roots of the above quadratic equation are the square root of 1936.

Also read: Properties of square numbers

How to Find the Square Root of 1936?

Now, we shall find the square root of 1936 using the prime factorisation and long division method.

Prime Factorisation Method

To find the square root of 1936 by the prime factorisation method, we first prime factorise 1936 and then make pairs of two to get the square root.

Prime factorisation of 1936 = 2 × 2 × 2 × 2 × 11 × 11

The square root of 1936 = √[2 × 2 × 2 × 2 × 11 × 11] = 2 × 2 × 11

Long Division Method

To find the square root of 1936 by the long division method, we shall write 1936 as the dividend and pair its digits from right to left. Now, we shall calculate the square root of 1936 as follows:

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 1936

Example 1:

Find the length and breadth of a rectangular plot whose area is 3872 m² and length is twice its breadth.

Solution:

Let ‘b’ be the breadth of the rectangular plot

Length of the rectangular plot = 2b

Area of the rectangular plot = length × breadth = 3872 m²

⇒ 2b × b = 3872

⇒ b² = 3872/2 = 1936

⇒ b = √1936 = 44 m (taking positive root as length cannot be negative)

∴ the length of the rectangular plot = 2 × 44 = 88 m

And the breadth of the rectangular plot= 44 m

Example 2:

Find the roots of the equation (x² + 314)/5 = 450.

Solution:

We have, (x² + 314)/5 = 450

⇒ x² + 314 = 2250

⇒ x² = 2250 – 314 = 1936

Taking the square roots on both side of the equation, we get,

⇒ x = √1936

⇒ x = ±44

Example 3:

Find the diameter of a circle whose area is 1936𝜋 cm².

Solution:

Let r be the radius of the circle.

Area of the circle = 𝜋r² = 1936𝜋 cm²

⇒ r² = 1936

⇒ r = √1936 = 44 (taking positive root as length cannot be negative)

∴ the diameter of the circle = 2 × 44 = 88 cm