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Square Root of 8000

The square root of 8000 is expressed as √8000 in the radical form and as (8000)^½ or (8000)^0.5 in the exponent form. The square root of 8000 rounded up to 9 decimal places is 89.442719100. It is the positive solution of the equation x² = 8000. We can express the square root of 8000 in its lowest radical form as 40 √5.

Square Root of 8000: 89.44271909999159
Square Root of 8000 in exponential form: (8000)^½ or (8000)^0.5
Square Root of 8000 in radical form: √8000 or 40 √5

Square Root of 8000

1.	What is the Square Root of 8000?
2.	How to find the Square Root of 8000?
3.	Is the Square Root of 8000 Irrational?
4.	FAQs

What is the Square Root of 8000?

The square root of 8000, (or root 8000), is the number which when multiplied by itself gives the product as 8000. Therefore, the square root of 8000 = √8000 = 40 √5 = 89.44271909999159.

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How to Find Square Root of 8000?

Square Root of 8000 by Long Division Method

Value of √8000 by Long Division Method

Explanation:

Forming pairs: 80 and 00
Find a number Y (8) such that whose square is <= 80. Now divide 80 by 8 with quotient as 8.
Bring down the next pair 00, to the right of the remainder 16. The new dividend is now 1600.
Add the last digit of the quotient (8) to the divisor (8) i.e. 8 + 8 = 16. To the right of 16, find a digit Z (which is 9) such that 16Z × Z <= 1600. After finding Z, together 16 and Z (9) form a new divisor 169 for the new dividend 1600.
Divide 1600 by 169 with the quotient as 9, giving the remainder = 1600 - 169 × 9 = 1600 - 1521 = 79.
Now, let's find the decimal places after the quotient 89.
Bring down 00 to the right of this remainder 79. The new dividend is now 7900.
Add the last digit of quotient to divisor i.e. 9 + 169 = 178. To the right of 178, find a digit Z (which is 4) such that 178Z × Z <= 7900. Together they form a new divisor (1784) for the new dividend (7900).
Divide 7900 by 1784 with the quotient as 4, giving the remainder = 7900 - 1784 × 4 = 7900 - 7136 = 764.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 8000.

Therefore, the square root of 8000 by long division method is 89.4 approximately.

Is Square Root of 8000 Irrational?

The actual value of √8000 is undetermined. The value of √8000 up to 25 decimal places is 89.44271909999158785636695. Hence, the square root of 8000 is an irrational number.

☛ Also Check:

Square Root of 69 - √69 = 8.30662
Square Root of 98 - √98 = 9.89949
Square Root of 841 - √841 = 29
Square Root of 40 - √40 = 6.32456
Square Root of 250 - √250 = 15.81139
Square Root of 48 - √48 = 6.92820
Square Root of 51 - √51 = 7.14143

Square Root of 8000 Solved Examples

Example 1: Solve the equation x² − 8000 = 0

Solution:

x² - 8000 = 0 i.e. x² = 8000
x = ±√8000
Since the value of the square root of 8000 is 89.443,
⇒ x = +√8000 or -√8000 = 89.443 or -89.443.
Example 2: If the surface area of a sphere is 32000π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 32000π in²
⇒ r = ±√8000 in
Since radius can't be negative,
⇒ r = √8000
The square root of 8000 is 89.443.
⇒ r = 89.443 in
Example 3: If the area of an equilateral triangle is 8000√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 = 8000√3 in²
⇒ a = ±√32000 in
Since length can't be negative,
⇒ a = √32000 = 2 √8000
We know that the square root of 8000 is 89.443.
⇒ a = 178.885 in

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FAQs on the Square Root of 8000

What is the Value of the Square Root of 8000?

The square root of 8000 is 89.44271.

Why is the Square Root of 8000 an Irrational Number?

Upon prime factorizing 8000 i.e. 2⁶ × 5³, 5 is in odd power. Therefore, the square root of 8000 is irrational.

What is the Square Root of -8000?

The square root of -8000 is an imaginary number. It can be written as √-8000 = √-1 × √8000 = i √8000 = 89.442i
where i = √-1 and it is called the imaginary unit.

Is the number 8000 a Perfect Square?

The prime factorization of 8000 = 2⁶ × 5³. Here, the prime factor 5 is not in the pair. Therefore, 8000 is not a perfect square.

What is the Value of 9 square root 8000?

The square root of 8000 is 89.443. Therefore, 9 √8000 = 9 × 89.443 = 804.984.

What is the Square Root of 8000 in Simplest Radical Form?

We need to express 8000 as the product of its prime factors i.e. 8000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5. Therefore, √8000 = √2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 = 40 √5. Thus, the square root of 8000 in the lowest radical form is 40 √5.

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