Square Root of 1872
The square root of 1872 is expressed as √1872 in the radical form and as (1872)½ or (1872)0.5 in the exponent form. The square root of 1872 rounded up to 6 decimal places is 43.266615. It is the positive solution of the equation x2 = 1872. We can express the square root of 1872 in its lowest radical form as 12 √13.
- Square Root of 1872: 43.266615305567875
- Square Root of 1872 in exponential form: (1872)½ or (1872)0.5
- Square Root of 1872 in radical form: √1872 or 12 √13
1. | What is the Square Root of 1872? |
2. | How to find the Square Root of 1872? |
3. | Is the Square Root of 1872 Irrational? |
4. | FAQs |
What is the Square Root of 1872?
The square root of 1872, (or root 1872), is the number which when multiplied by itself gives the product as 1872. Therefore, the square root of 1872 = √1872 = 12 √13 = 43.266615305567875.
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How to Find Square Root of 1872?
Value of √1872 by Long Division Method
Explanation:
- Forming pairs: 18 and 72
- 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 72, to the right of the remainder 2. The new dividend is now 272.
- 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 <= 272. After finding Z, together 8 and Z (3) form a new divisor 83 for the new dividend 272.
- Divide 272 by 83 with the quotient as 3, giving the remainder = 272 - 83 × 3 = 272 - 249 = 23.
- Now, let's find the decimal places after the quotient 43.
- Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
- Add the last digit of quotient to divisor i.e. 3 + 83 = 86. To the right of 86, find a digit Z (which is 2) such that 86Z × Z <= 2300. Together they form a new divisor (862) for the new dividend (2300).
- Divide 2300 by 862 with the quotient as 2, giving the remainder = 2300 - 862 × 2 = 2300 - 1724 = 576.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1872.
Therefore, the square root of 1872 by long division method is 43.2 approx.
Is Square Root of 1872 Irrational?
The actual value of √1872 is undetermined. The value of √1872 up to 25 decimal places is 43.26661530556787151743066. Hence, the square root of 1872 is an irrational number.
☛ Also Check:
- Square Root of 50 - √50 = 7.07107
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- Square Root of 22 - √22 = 4.69042
- Square Root of 99 - √99 = 9.94987
- Square Root of 240 - √240 = 15.49193
- Square Root of 90 - √90 = 9.48683
- Square Root of 192 - √192 = 13.85641
Square Root of 1872 Solved Examples
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Example 1: Solve the equation x2 − 1872 = 0
Solution:
x2 - 1872 = 0 i.e. x2 = 1872
x = ±√1872
Since the value of the square root of 1872 is 43.267,
⇒ x = +√1872 or -√1872 = 43.267 or -43.267. -
Example 2: If the surface area of a cube is 11232 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 = 11232 in2
⇒ a = ±√1872 in
Since length can't be negative,
⇒ a = √1872
We know that the square root of 1872 is 43.267.
⇒ a = 43.267 in -
Example 3: If the surface area of a sphere is 7488π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 7488π in2
⇒ r = ±√1872 in
Since radius can't be negative,
⇒ r = √1872
The square root of 1872 is 43.267.
⇒ r = 43.267 in
FAQs on the Square Root of 1872
What is the Value of the Square Root of 1872?
The square root of 1872 is 43.26661.
Why is the Square Root of 1872 an Irrational Number?
Upon prime factorizing 1872 i.e. 24 × 32 × 131, 13 is in odd power. Therefore, the square root of 1872 is irrational.
Is the number 1872 a Perfect Square?
The prime factorization of 1872 = 24 × 32 × 131. Here, the prime factor 13 is not in the pair. Therefore, 1872 is not a perfect square.
What is the Value of 3 square root 1872?
The square root of 1872 is 43.267. Therefore, 3 √1872 = 3 × 43.267 = 129.800.
Evaluate 19 plus 3 square root 1872
The given expression is 19 + 3 √1872. We know that the square root of 1872 is 43.267. Therefore, 19 + 3 √1872 = 19 + 3 × 43.267 = 19 + 129.800 = 148.800
If the Square Root of 1872 is 43.267. Find the Value of the Square Root of 18.72.
Let us represent √18.72 in p/q form i.e. √(1872/100) = 18.72/10 = 4.327. Hence, the value of √18.72 = 4.327
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