Square Root of 2250
The square root of 2250 is expressed as √2250 in the radical form and as (2250)½ or (2250)0.5 in the exponent form. The square root of 2250 rounded up to 7 decimal places is 47.4341649. It is the positive solution of the equation x2 = 2250. We can express the square root of 2250 in its lowest radical form as 15 √10.
- Square Root of 2250: 47.43416490252569
- Square Root of 2250 in exponential form: (2250)½ or (2250)0.5
- Square Root of 2250 in radical form: √2250 or 15 √10
1. | What is the Square Root of 2250? |
2. | How to find the Square Root of 2250? |
3. | Is the Square Root of 2250 Irrational? |
4. | FAQs |
What is the Square Root of 2250?
The square root of 2250, (or root 2250), is the number which when multiplied by itself gives the product as 2250. Therefore, the square root of 2250 = √2250 = 15 √10 = 47.43416490252569.
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How to Find Square Root of 2250?
Value of √2250 by Long Division Method
Explanation:
- Forming pairs: 22 and 50
- Find a number Y (4) such that whose square is <= 22. Now divide 22 by 4 with quotient as 4.
- Bring down the next pair 50, to the right of the remainder 6. The new dividend is now 650.
- 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 7) such that 8Z × Z <= 650. After finding Z, together 8 and Z (7) form a new divisor 87 for the new dividend 650.
- Divide 650 by 87 with the quotient as 7, giving the remainder = 650 - 87 × 7 = 650 - 609 = 41.
- Now, let's find the decimal places after the quotient 47.
- Bring down 00 to the right of this remainder 41. The new dividend is now 4100.
- Add the last digit of quotient to divisor i.e. 7 + 87 = 94. To the right of 94, find a digit Z (which is 4) such that 94Z × Z <= 4100. Together they form a new divisor (944) for the new dividend (4100).
- Divide 4100 by 944 with the quotient as 4, giving the remainder = 4100 - 944 × 4 = 4100 - 3776 = 324.
- Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 2250.
Therefore, the square root of 2250 by long division method is 47.4 approx.
Is Square Root of 2250 Irrational?
The actual value of √2250 is undetermined. The value of √2250 up to 25 decimal places is 47.43416490252568997998340. Hence, the square root of 2250 is an irrational number.
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- Square Root of 361 - √361 = 19
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- Square Root of 74 - √74 = 8.60233
- Square Root of 125 - √125 = 11.18034
- Square Root of 12 - √12 = 3.46410
- Square Root of 512 - √512 = 22.62742
Square Root of 2250 Solved Examples
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Example 1: Solve the equation x2 − 2250 = 0
Solution:
x2 - 2250 = 0 i.e. x2 = 2250
x = ±√2250
Since the value of the square root of 2250 is 47.434,
⇒ x = +√2250 or -√2250 = 47.434 or -47.434. -
Example 2: If the area of an equilateral triangle is 2250√3 in2. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a2 = 2250√3 in2
⇒ a = ±√9000 in
Since length can't be negative,
⇒ a = √9000 = 2 √2250
We know that the square root of 2250 is 47.434.
⇒ a = 94.868 in -
Example 3: If the surface area of a sphere is 9000π in2. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr2 = 9000π in2
⇒ r = ±√2250 in
Since radius can't be negative,
⇒ r = √2250
The square root of 2250 is 47.434.
⇒ r = 47.434 in
FAQs on the Square Root of 2250
What is the Value of the Square Root of 2250?
The square root of 2250 is 47.43416.
Why is the Square Root of 2250 an Irrational Number?
Upon prime factorizing 2250 i.e. 21 × 32 × 53, 2 is in odd power. Therefore, the square root of 2250 is irrational.
Evaluate 20 plus 19 square root 2250
The given expression is 20 + 19 √2250. We know that the square root of 2250 is 47.434. Therefore, 20 + 19 √2250 = 20 + 19 × 47.434 = 20 + 901.249 = 921.249
What is the Value of 8 square root 2250?
The square root of 2250 is 47.434. Therefore, 8 √2250 = 8 × 47.434 = 379.473.
Is the number 2250 a Perfect Square?
The prime factorization of 2250 = 21 × 32 × 53. Here, the prime factor 2 is not in the pair. Therefore, 2250 is not a perfect square.
What is the Square Root of -2250?
The square root of -2250 is an imaginary number. It can be written as √-2250 = √-1 × √2250 = i √2250 = 47.434i
where i = √-1 and it is called the imaginary unit.
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