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Square Root of 133

The square root of 133 is expressed as √133 in the radical form and as (133)½ or (133)0.5 in the exponent form. The square root of 133 rounded up to 8 decimal places is 11.53256259. It is the positive solution of the equation x2 = 133.

  • Square Root of 133: 11.532562594670797
  • Square Root of 133 in exponential form: (133)½ or (133)0.5
  • Square Root of 133 in radical form: √133

Square Root of 133

1. What is the Square Root of 133?
2. How to find the Square Root of 133?
3. Is the Square Root of 133 Irrational?
4. FAQs

What is the Square Root of 133?

The square root of 133, (or root 133), is the number which when multiplied by itself gives the product as 133. Therefore, the square root of 133 = √133 = 11.532562594670797.

☛ Check: Square Root Calculator

How to Find Square Root of 133?

Square Root of 133 by Long Division Method

Value of √133 by Long Division Method

Explanation:

  • Forming pairs: 01 and 33
  • 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 33, to the right of the remainder 0. The new dividend is now 33.
  • 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 <= 33. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 33.
  • Divide 33 by 21 with the quotient as 1, giving the remainder = 33 - 21 × 1 = 33 - 21 = 12.
  • Now, let's find the decimal places after the quotient 11.
  • Bring down 00 to the right of this remainder 12. The new dividend is now 1200.
  • Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 5) such that 22Z × Z <= 1200. Together they form a new divisor (225) for the new dividend (1200).
  • Divide 1200 by 225 with the quotient as 5, giving the remainder = 1200 - 225 × 5 = 1200 - 1125 = 75.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 133.

Therefore, the square root of 133 by long division method is 11.5 approx.

Is Square Root of 133 Irrational?

The actual value of √133 is undetermined. The value of √133 up to 25 decimal places is 11.53256259467079588935418. Hence, the square root of 133 is an irrational number.

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Square Root of 133 Solved Examples

  1. Example 1: Solve the equation x2 − 133 = 0

    Solution:

    x2 - 133 = 0 i.e. x2 = 133
    x = ±√133
    Since the value of the square root of 133 is 11.533,
    ⇒ x = +√133 or -√133 = 11.533 or -11.533.

  2. Example 2: If the area of a circle is 133π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 133π in2
    ⇒ r = ±√133 in
    Since radius can't be negative,
    ⇒ r = √133
    The square root of 133 is 11.533.
    ⇒ r = 11.533 in

  3. Example 3: If the surface area of a sphere is 532π in2. Find the radius of the sphere.

    Solution:

    Let 'r' be the radius of the sphere.
    ⇒ Area of the sphere = 4πr2 = 532π in2
    ⇒ r = ±√133 in
    Since radius can't be negative,
    ⇒ r = √133
    The square root of 133 is 11.533.
    ⇒ r = 11.533 in

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FAQs on the Square Root of 133

What is the Value of the Square Root of 133?

The square root of 133 is 11.53256.

Why is the Square Root of 133 an Irrational Number?

Upon prime factorizing 133 i.e. 71 × 191, 7 is in odd power. Therefore, the square root of 133 is irrational.

What is the Square of the Square Root of 133?

The square of the square root of 133 is the number 133 itself i.e. (√133)2 = (133)2/2 = 133.

What is the Square Root of -133?

The square root of -133 is an imaginary number. It can be written as √-133 = √-1 × √133 = i √133 = 11.532i
where i = √-1 and it is called the imaginary unit.

Is the number 133 a Perfect Square?

The prime factorization of 133 = 71 × 191. Here, the prime factor 7 is not in the pair. Therefore, 133 is not a perfect square.

What is the Value of 3 square root 133?

The square root of 133 is 11.533. Therefore, 3 √133 = 3 × 11.533 = 34.598.

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