Square Root of 5000
The square root of 5000 is expressed as √5000 in the radical form and as (5000)^{½} or (5000)^{0.5} in the exponent form. The square root of 5000 rounded up to 5 decimal places is 70.71068. It is the positive solution of the equation x^{2} = 5000. We can express the square root of 5000 in its lowest radical form as 50 √2.
 Square Root of 5000: 70.71067811865476
 Square Root of 5000 in exponential form: (5000)^{½} or (5000)^{0.5}
 Square Root of 5000 in radical form: √5000 or 50 √2
1.  What is the Square Root of 5000? 
2.  How to find the Square Root of 5000? 
3.  Is the Square Root of 5000 Irrational? 
4.  FAQs 
What is the Square Root of 5000?
The square root of 5000, (or root 5000), is the number which when multiplied by itself gives the product as 5000. Therefore, the square root of 5000 = √5000 = 50 √2 = 70.71067811865476.
☛ Check: Square Root Calculator
How to Find Square Root of 5000?
Value of √5000 by Long Division Method
Explanation:
 Forming pairs: 50 and 00
 Find a number Y (7) such that whose square is <= 50. Now divide 50 by 7 with quotient as 7.
 Bring down the next pair 00, to the right of the remainder 1. The new dividend is now 100.
 Add the last digit of the quotient (7) to the divisor (7) i.e. 7 + 7 = 14. To the right of 14, find a digit Z (which is 0) such that 14Z × Z <= 100. After finding Z, together 14 and Z (0) form a new divisor 140 for the new dividend 100.
 Divide 100 by 140 with the quotient as 0, giving the remainder = 100  140 × 0 = 100  0 = 100.
 Now, let's find the decimal places after the quotient 70.
 Bring down 00 to the right of this remainder 100. The new dividend is now 10000.
 Add the last digit of quotient to divisor i.e. 0 + 140 = 140. To the right of 140, find a digit Z (which is 7) such that 140Z × Z <= 10000. Together they form a new divisor (1407) for the new dividend (10000).
 Divide 10000 by 1407 with the quotient as 7, giving the remainder = 10000  1407 × 7 = 10000  9849 = 151.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 5000.
Therefore, the square root of 5000 by long division method is 70.7 approximately.
Is Square Root of 5000 Irrational?
The actual value of √5000 is undetermined. The value of √5000 up to 25 decimal places is 70.71067811865475244008444. Hence, the square root of 5000 is an irrational number.
☛ Also Check:
 Square Root of 8  √8 = 2.82843
 Square Root of 106  √106 = 10.29563
 Square Root of 361  √361 = 19
 Square Root of 28  √28 = 5.29150
 Square Root of 289  √289 = 17
 Square Root of 16  √16 = 4
 Square Root of 196  √196 = 14
Square Root of 5000 Solved Examples

Example 1: Solve the equation x^{2} − 5000 = 0
Solution:
x^{2}  5000 = 0 i.e. x^{2} = 5000
x = ±√5000
Since the value of the square root of 5000 is 70.711,
⇒ x = +√5000 or √5000 = 70.711 or 70.711. 
Example 2: If the surface area of a cube is 30000 in^{2}. 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 = 6a^{2} = 30000 in^{2}
⇒ a = ±√5000 in
Since length can't be negative,
⇒ a = √5000
We know that the square root of 5000 is 70.711.
⇒ a = 70.711 in 
Example 3: If the area of a circle is 5000π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 5000π in^{2}
⇒ r = ±√5000 in
Since radius can't be negative,
⇒ r = √5000
The square root of 5000 is 70.711.
⇒ r = 70.711 in
FAQs on the Square Root of 5000
What is the Value of the Square Root of 5000?
The square root of 5000 is 70.71067.
Why is the Square Root of 5000 an Irrational Number?
Upon prime factorizing 5000 i.e. 2^{3} × 5^{4}, 2 is in odd power. Therefore, the square root of 5000 is irrational.
What is the Square Root of 5000?
The square root of 5000 is an imaginary number. It can be written as √5000 = √1 × √5000 = i √5000 = 70.71i
where i = √1 and it is called the imaginary unit.
What is the Square of the Square Root of 5000?
The square of the square root of 5000 is the number 5000 itself i.e. (√5000)^{2} = (5000)^{2/2} = 5000.
If the Square Root of 5000 is 70.711. Find the Value of the Square Root of 50.
Let us represent √50 in p/q form i.e. √(5000/100) = 50/10 = 7.071. Hence, the value of √50.0 = 7.071
What is the Value of 8 square root 5000?
The square root of 5000 is 70.711. Therefore, 8 √5000 = 8 × 70.711 = 565.685.
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