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Square Root of 139

The square root of 139 is expressed as √139 in the radical form and as (139)½ or (139)0.5 in the exponent form. The square root of 139 rounded up to 6 decimal places is 11.789826. It is the positive solution of the equation x2 = 139.

  • Square Root of 139: 11.789826122551595
  • Square Root of 139 in exponential form: (139)½ or (139)0.5
  • Square Root of 139 in radical form: √139

Square Root of 139

1. What is the Square Root of 139?
2. How to find the Square Root of 139?
3. Is the Square Root of 139 Irrational?
4. FAQs

What is the Square Root of 139?

The square root of 139, (or root 139), is the number which when multiplied by itself gives the product as 139. Therefore, the square root of 139 = √139 = 11.789826122551595.

☛ Check: Square Root Calculator

How to Find Square Root of 139?

Square Root of 139 by Long Division Method

Value of √139 by Long Division Method

Explanation:

  • Forming pairs: 01 and 39
  • Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
  • Bring down the next pair 39, to the right of the remainder 0. The new dividend is now 39.
  • Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 1) such that 2Z × Z <= 39. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 39.
  • Divide 39 by 21 with the quotient as 1, giving the remainder = 39 - 21 × 1 = 39 - 21 = 18.
  • Now, let's find the decimal places after the quotient 11.
  • Bring down 00 to the right of this remainder 18. The new dividend is now 1800.
  • Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 7) such that 22Z × Z <= 1800. Together they form a new divisor (227) for the new dividend (1800).
  • Divide 1800 by 227 with the quotient as 7, giving the remainder = 1800 - 227 × 7 = 1800 - 1589 = 211.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 139.

Therefore, the square root of 139 by long division method is 11.7 approximately.

Is Square Root of 139 Irrational?

The actual value of √139 is undetermined. The value of √139 up to 25 decimal places is 11.78982612255159596846918. Hence, the square root of 139 is an irrational number.

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Square Root of 139 Solved Examples

  1. Example 1: Solve the equation x2 − 139 = 0

    Solution:

    x2 - 139 = 0 i.e. x2 = 139
    x = ±√139
    Since the value of the square root of 139 is 11.790,
    ⇒ x = +√139 or -√139 = 11.790 or -11.790.

  2. Example 2: If the surface area of a cube is 834 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 = 834 in2
    ⇒ a = ±√139 in
    Since length can't be negative,
    ⇒ a = √139
    We know that the square root of 139 is 11.790.
    ⇒ a = 11.790 in

  3. Example 3: If the surface area of a sphere is 556π in2. Find the radius of the sphere.

    Solution:

    Let 'r' be the radius of the sphere.
    ⇒ Area of the sphere = 4πr2 = 556π in2
    ⇒ r = ±√139 in
    Since radius can't be negative,
    ⇒ r = √139
    The square root of 139 is 11.790.
    ⇒ r = 11.790 in

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FAQs on the Square Root of 139

What is the Value of the Square Root of 139?

The square root of 139 is 11.78982.

Why is the Square Root of 139 an Irrational Number?

The number 139 is prime. This implies that the number 139 is pairless and is not in the power of 2. Therefore, the square root of 139 is irrational.

What is the Square Root of 139 in Simplest Radical Form?

The number 139 is a prime number. This implies that the number 139 is pairless and is not in the power of 2. Therefore, the radical form of square root of 139 cannot be simplified further.

What is the Square Root of -139?

The square root of -139 is an imaginary number. It can be written as √-139 = √-1 × √139 = i √139 = 11.789i
where i = √-1 and it is called the imaginary unit.

What is the Square of the Square Root of 139?

The square of the square root of 139 is the number 139 itself i.e. (√139)2 = (139)2/2 = 139.

Evaluate 3 plus 9 square root 139

The given expression is 3 + 9 √139. We know that the square root of 139 is 11.790. Therefore, 3 + 9 √139 = 3 + 9 × 11.790 = 3 + 106.108 = 109.108

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