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Square Root 36
Square Root 36

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Square Root of 1936

The square root of 1936 is expressed as √1936 in the radical form and as (1936)½ or (1936)0.5 in the exponent form. The square root of 1936 is 44. It is the positive solution of the equation x2 = 1936. The number 1936 is a perfect square.

  • Square Root of 1936: 44
  • Square Root of 1936 in exponential form: (1936)½ or (1936)0.5
  • Square Root of 1936 in radical form: √1936
1. What is the Square Root of 1936?
2. How to find the Square Root of 1936?
3. Is the Square Root of 1936 Rational?
4. FAQs

What is the Square Root of 1936?

The square root of 1936, (or root 1936), is the number which when multiplied by itself gives the product as 1936. Therefore, the square root of 1936 = √1936 = 44.

☛ Check: Square Root Calculator

How to Find Square Root of 1936?

Value of √1936 by Long Division Method

Explanation:

  • Forming pairs: 19 and 36
  • Find a number Y (4) such that whose square is <= 19. Now divide 19 by 4 with quotient as 4.
  • Bring down the next pair 36, to the right of the remainder 3. The new dividend is now 336.
  • Add the last digit of the quotient (4) to the divisor (4) i.e. 4 + 4 = 8. To the right of 8, find a digit Z (which is 4) such that 8Z × Z <= 336. After finding Z, together 8 and Z (4) form a new divisor 84 for the new dividend 336.
  • Divide 336 by 84 with the quotient as 4, giving the remainder = 336 – 84 × 4 = 336 – 336 = 0.
  • We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 1936 by long division method is 44.

Is Square Root of 1936 Rational?

The value of √1936 is 44. Hence, the square root of 1936 is a rational number.

☛ Also Check:

  • Square Root of 784 – √784 = 28
  • Square Root of 250 – √250 = 15.81139
  • Square Root of 169 – √169 = 13
  • Square Root of 16 – √16 = 4
  • Square Root of 37 – √37 = 6.08276
  • Square Root of 100 – √100 = 10
  • Square Root of 324 – √324 = 18

Square Root of 1936 Solved Examples

  1. Example 1: Solve the equation x2 − 1936 = 0

    Solution:

    x2 – 1936 = 0 i.e. x2 = 1936

    x = ±√1936
    Since the value of the square root of 1936 is 44,
    ⇒ x = +√1936 or -√1936 = 44 or -44.

  2. Example 2: If the surface area of a cube is 11616 in2. Find the length of the side of the cube.

    Solution:

    Let ‘a’ be the length of the side of the cube.

    ⇒ Area of the cube = 6a2 = 11616 in2
    ⇒ a = ±√1936 in
    Since length can’t be negative,
    ⇒ a = √1936
    We know that the square root of 1936 is 44.
    ⇒ a = 44 in

  3. Example 3: If the area of a square is 1936 in2. Find the length of the side of the square.

    Solution:

    Let ‘a’ be the length of the side of the square.

    ⇒ Area of the square = a2 = 1936 in2
    ⇒ a = ±√1936 in
    Since length can’t be negative,
    ⇒ a = √1936 = 44 in

FAQs on the Square Root of 1936

What is the Value of the Square Root of 1936?

The square root of 1936 is 44.

Why is the Square Root of 1936 a Rational Number?

Upon prime factorizing 1936 i.e. 24 × 112, we find that all the prime factors are in even power. This implies that the square root of 1936 is a positive integer. Therefore, the square root of 1936 is rational.

What is the Square of the Square Root of 1936?

The square of the square root of 1936 is the number 1936 itself i.e. (√1936)2 = (1936)2/2 = 1936.

Evaluate 10 plus 15 square root 1936

The given expression is 10 + 15 √1936. We know that the square root of 1936 is 44. Therefore, 10 + 15 √1936 = 10 + 15 × 44 = 10 + 660 = 670

What is the Square Root of -1936?

The square root of -1936 is an imaginary number. It can be written as √-1936 = √-1 × √1936 = i √1936 = 44i
where i = √-1 and it is called the imaginary unit.

Is the number 1936 a Perfect Square?

The prime factorization of 1936 = 24 × 112. Here, all the numbers are in the power of 2. This implies that the square root of 1936 is a positive integer. Therefore, 1936 is a perfect square.

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