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Square Root of 4000

The square root of 4000 is expressed as √4000 in the radical form and as (4000)½ or (4000)0.5 in the exponent form. The square root of 4000 rounded up to 8 decimal places is 63.24555320. It is the positive solution of the equation x2 = 4000. We can express the square root of 4000 in its lowest radical form as 20 √10.

  • Square Root of 4000: 63.245553203367585
  • Square Root of 4000 in exponential form: (4000)½ or (4000)0.5
  • Square Root of 4000 in radical form: √4000 or 20 √10

Square Root of 4000

1. What is the Square Root of 4000?
2. How to find the Square Root of 4000?
3. Is the Square Root of 4000 Irrational?
4. FAQs

What is the Square Root of 4000?

The square root of 4000, (or root 4000), is the number which when multiplied by itself gives the product as 4000. Therefore, the square root of 4000 = √4000 = 20 √10 = 63.245553203367585.

☛ Check: Square Root Calculator

How to Find Square Root of 4000?

Square Root of 4000 by Long Division Method

Value of √4000 by Long Division Method

Explanation:

  • Forming pairs: 40 and 00
  • Find a number Y (6) such that whose square is <= 40. Now divide 40 by 6 with quotient as 6.
  • Bring down the next pair 00, to the right of the remainder 4. The new dividend is now 400.
  • Add the last digit of the quotient (6) to the divisor (6) i.e. 6 + 6 = 12. To the right of 12, find a digit Z (which is 3) such that 12Z × Z <= 400. After finding Z, together 12 and Z (3) form a new divisor 123 for the new dividend 400.
  • Divide 400 by 123 with the quotient as 3, giving the remainder = 400 - 123 × 3 = 400 - 369 = 31.
  • Now, let's find the decimal places after the quotient 63.
  • Bring down 00 to the right of this remainder 31. The new dividend is now 3100.
  • Add the last digit of quotient to divisor i.e. 3 + 123 = 126. To the right of 126, find a digit Z (which is 2) such that 126Z × Z <= 3100. Together they form a new divisor (1262) for the new dividend (3100).
  • Divide 3100 by 1262 with the quotient as 2, giving the remainder = 3100 - 1262 × 2 = 3100 - 2524 = 576.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 4000.

Therefore, the square root of 4000 by long division method is 63.2 approximately.

Is Square Root of 4000 Irrational?

The actual value of √4000 is undetermined. The value of √4000 up to 25 decimal places is 63.24555320336758663997787. Hence, the square root of 4000 is an irrational number.

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Square Root of 4000 Solved Examples

  1. Example 1: Solve the equation x2 − 4000 = 0

    Solution:

    x2 - 4000 = 0 i.e. x2 = 4000
    x = ±√4000
    Since the value of the square root of 4000 is 63.246,
    ⇒ x = +√4000 or -√4000 = 63.246 or -63.246.

  2. Example 2: If the area of a square is 4000 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 = 4000 in2
    ⇒ a = ±√4000 in
    Since length can't be negative,
    ⇒ a = √4000 = 63.246 in

  3. Example 3: If the surface area of a cube is 24000 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 = 24000 in2
    ⇒ a = ±√4000 in
    Since length can't be negative,
    ⇒ a = √4000
    We know that the square root of 4000 is 63.246.
    ⇒ a = 63.246 in

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FAQs on the Square Root of 4000

What is the Value of the Square Root of 4000?

The square root of 4000 is 63.24555.

Why is the Square Root of 4000 an Irrational Number?

Upon prime factorizing 4000 i.e. 25 × 53, 2 is in odd power. Therefore, the square root of 4000 is irrational.

If the Square Root of 4000 is 63.246. Find the Value of the Square Root of 40.

Let us represent √40 in p/q form i.e. √(4000/100) = 40/10 = 6.325. Hence, the value of √40.0 = 6.325

Is the number 4000 a Perfect Square?

The prime factorization of 4000 = 25 × 53. Here, the prime factor 2 is not in the pair. Therefore, 4000 is not a perfect square.

What is the Square Root of -4000?

The square root of -4000 is an imaginary number. It can be written as √-4000 = √-1 × √4000 = i √4000 = 63.245i
where i = √-1 and it is called the imaginary unit.

Evaluate 6 plus 20 square root 4000

The given expression is 6 + 20 √4000. We know that the square root of 4000 is 63.246. Therefore, 6 + 20 √4000 = 6 + 20 × 63.246 = 6 + 1264.911 = 1270.911

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