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Square Root of 1875

The square root of 1875 is expressed as √1875 in the radical form and as (1875)½ or (1875)0.5 in the exponent form. The square root of 1875 rounded up to 9 decimal places is 43.301270189. It is the positive solution of the equation x2 = 1875. We can express the square root of 1875 in its lowest radical form as 25 √3.

  • Square Root of 1875: 43.30127018922193
  • Square Root of 1875 in exponential form: (1875)½ or (1875)0.5
  • Square Root of 1875 in radical form: √1875 or 25 √3

Square Root of 1875

1. What is the Square Root of 1875?
2. How to find the Square Root of 1875?
3. Is the Square Root of 1875 Irrational?
4. FAQs

What is the Square Root of 1875?

The square root of 1875, (or root 1875), is the number which when multiplied by itself gives the product as 1875. Therefore, the square root of 1875 = √1875 = 25 √3 = 43.30127018922193.

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How to Find Square Root of 1875?

Square Root of 1875 by Long Division Method

Value of √1875 by Long Division Method

Explanation:

  • Forming pairs: 18 and 75
  • Find a number Y (4) such that whose square is <= 18. Now divide 18 by 4 with quotient as 4.
  • Bring down the next pair 75, to the right of the remainder 2. The new dividend is now 275.
  • 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 3) such that 8Z × Z <= 275. After finding Z, together 8 and Z (3) form a new divisor 83 for the new dividend 275.
  • Divide 275 by 83 with the quotient as 3, giving the remainder = 275 - 83 × 3 = 275 - 249 = 26.
  • Now, let's find the decimal places after the quotient 43.
  • Bring down 00 to the right of this remainder 26. The new dividend is now 2600.
  • Add the last digit of quotient to divisor i.e. 3 + 83 = 86. To the right of 86, find a digit Z (which is 3) such that 86Z × Z <= 2600. Together they form a new divisor (863) for the new dividend (2600).
  • Divide 2600 by 863 with the quotient as 3, giving the remainder = 2600 - 863 × 3 = 2600 - 2589 = 11.
  • Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1875.

Therefore, the square root of 1875 by long division method is 43.3 approximately.

Is Square Root of 1875 Irrational?

The actual value of √1875 is undetermined. The value of √1875 up to 25 decimal places is 43.30127018922193233818616. Hence, the square root of 1875 is an irrational number.

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Square Root of 1875 Solved Examples

  1. Example 1: Solve the equation x2 − 1875 = 0

    Solution:

    x2 - 1875 = 0 i.e. x2 = 1875
    x = ±√1875
    Since the value of the square root of 1875 is 43.301,
    ⇒ x = +√1875 or -√1875 = 43.301 or -43.301.

  2. Example 2: If the area of a circle is 1875π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 1875π in2
    ⇒ r = ±√1875 in
    Since radius can't be negative,
    ⇒ r = √1875
    The square root of 1875 is 43.301.
    ⇒ r = 43.301 in

  3. Example 3: If the surface area of a cube is 11250 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 = 11250 in2
    ⇒ a = ±√1875 in
    Since length can't be negative,
    ⇒ a = √1875
    We know that the square root of 1875 is 43.301.
    ⇒ a = 43.301 in

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FAQs on the Square Root of 1875

What is the Value of the Square Root of 1875?

The square root of 1875 is 43.30127.

Why is the Square Root of 1875 an Irrational Number?

Upon prime factorizing 1875 i.e. 31 × 54, 3 is in odd power. Therefore, the square root of 1875 is irrational.

What is the Square Root of -1875?

The square root of -1875 is an imaginary number. It can be written as √-1875 = √-1 × √1875 = i √1875 = 43.301i
where i = √-1 and it is called the imaginary unit.

Evaluate 13 plus 8 square root 1875

The given expression is 13 + 8 √1875. We know that the square root of 1875 is 43.301. Therefore, 13 + 8 √1875 = 13 + 8 × 43.301 = 13 + 346.410 = 359.410

What is the Value of 1 square root 1875?

The square root of 1875 is 43.301. Therefore, 1 √1875 = 1 × 43.301 = 43.301.

What is the Square of the Square Root of 1875?

The square of the square root of 1875 is the number 1875 itself i.e. (√1875)2 = (1875)2/2 = 1875.

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