Square Root of 2500
The square root of 2500 is expressed as √2500 in the radical form and as (2500)½ or (2500)0.5 in the exponent form. The square root of 2500 is 50. It is the positive solution of the equation x2 = 2500. The number 2500 is a perfect square.
- Square Root of 2500: 50
- Square Root of 2500 in exponential form: (2500)½ or (2500)0.5
- Square Root of 2500 in radical form: √2500
1. | What is the Square Root of 2500? |
2. | How to find the Square Root of 2500? |
3. | Is the Square Root of 2500 Rational? |
4. | FAQs |
What is the Square Root of 2500?
The square root of 2500, (or root 2500), is the number which when multiplied by itself gives the product as 2500. Therefore, the square root of 2500 = √2500 = 50.
☛ Check: Square Root Calculator
How to Find Square Root of 2500?
Value of √2500 by Long Division Method
Explanation:
- Forming pairs: 25 and 00
- Find a number Y (5) such that whose square is <= 25. Now divide 25 by 5 with quotient as 5.
- Bring down the next pair 00, to the right of the remainder 0. The new dividend is now 0.
- Add the last digit of the quotient (5) to the divisor (5) i.e. 5 + 5 = 10. To the right of 10, find a digit Z (which is 0) such that 10Z × Z <= 0. After finding Z, together 10 and Z (0) form a new divisor 100 for the new dividend 0.
- Divide 0 by 100 with the quotient as 0, giving the remainder = 0 - 100 × 0 = 0 - 0 = 0.
- We stop the process since the remainder is now 0 and there are no more digits that can be brought down.
Therefore, the square root of 2500 by long division method is 50.
Is Square Root of 2500 Rational?
The value of √2500 is 50. Hence, the square root of 2500 is a rational number.
☛ Also Check:
- Square Root of 76 - √76 = 8.71780
- Square Root of 26 - √26 = 5.09902
- Square Root of 49 - √49 = 7
- Square Root of 140 - √140 = 11.83216
- Square Root of 51 - √51 = 7.14143
- Square Root of 97 - √97 = 9.84886
- Square Root of 162 - √162 = 12.72792
Square Root of 2500 Solved Examples
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Example 1: Solve the equation x2 − 2500 = 0
Solution:
x2 - 2500 = 0 i.e. x2 = 2500
x = ±√2500
Since the value of the square root of 2500 is 50,
⇒ x = +√2500 or -√2500 = 50 or -50. -
Example 2: If the area of an equilateral triangle is 2500√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 = 2500√3 in2
⇒ a = ±√10000 in
Since length can't be negative,
⇒ a = √10000 = 2 √2500
We know that the square root of 2500 is 50.
⇒ a = 100 in -
Example 3: If the area of a circle is 2500π in2. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr2 = 2500π in2
⇒ r = ±√2500 in
Since radius can't be negative,
⇒ r = √2500
Square root of 2500 is 50.
⇒ r = 50 in
FAQs on the Square Root of 2500
What is the Value of the Square Root of 2500?
The square root of 2500 is 50.
Why is the Square Root of 2500 a Rational Number?
Upon prime factorizing 2500 i.e. 22 × 54, we find that all the prime factors are in even power. This implies that the square root of 2500 is a positive integer. Therefore, the square root of 2500 is rational.
If the Square Root of 2500 is 50. Find the Value of the Square Root of 25.
Let us represent √25 in p/q form i.e. √(2500/100) = 25/10 = 5. Hence, the value of √25 = 5
What is the Square Root of -2500?
The square root of -2500 is an imaginary number. It can be written as √-2500 = √-1 × √2500 = i √2500 = 50i
where i = √-1 and it is called the imaginary unit.
What is the Square of the Square Root of 2500?
The square of the square root of 2500 is the number 2500 itself i.e. (√2500)2 = (2500)2/2 = 2500.
Is the number 2500 a Perfect Square?
The prime factorization of 2500 = 22 × 54. Here, all the numbers are in the power of 2. This implies that the square root of 2500 is a positive integer. Therefore, 2500 is a perfect square.
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