Square Root of 6000

The square root of 6000 is expressed as √6000 in the radical form and as (6000)^½ or (6000)^0.5 in the exponent form. The square root of 6000 rounded up to 6 decimal places is 77.459667. It is the positive solution of the equation x² = 6000. We can express the square root of 6000 in its lowest radical form as 20 √15.

Square Root of 6000: 77.45966692414834
Square Root of 6000 in exponential form: (6000)^½ or (6000)^0.5
Square Root of 6000 in radical form: √6000 or 20 √15

Square Root of 6000

1.	What is the Square Root of 6000?
2.	How to find the Square Root of 6000?
3.	Is the Square Root of 6000 Irrational?
4.	FAQs

What is the Square Root of 6000?

The square root of 6000, (or root 6000), is the number which when multiplied by itself gives the product as 6000. Therefore, the square root of 6000 = √6000 = 20 √15 = 77.45966692414834.

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How to Find Square Root of 6000?

Square Root of 6000 by Long Division Method

Value of √6000 by Long Division Method

Explanation:

Forming pairs: 60 and 00
Find a number Y (7) such that whose square is <= 60. Now divide 60 by 7 with quotient as 7.
Bring down the next pair 00, to the right of the remainder 11. The new dividend is now 1100.
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 7) such that 14Z × Z <= 1100. After finding Z, together 14 and Z (7) form a new divisor 147 for the new dividend 1100.
Divide 1100 by 147 with the quotient as 7, giving the remainder = 1100 - 147 × 7 = 1100 - 1029 = 71.
Now, let's find the decimal places after the quotient 77.
Bring down 00 to the right of this remainder 71. The new dividend is now 7100.
Add the last digit of quotient to divisor i.e. 7 + 147 = 154. To the right of 154, find a digit Z (which is 4) such that 154Z × Z <= 7100. Together they form a new divisor (1544) for the new dividend (7100).
Divide 7100 by 1544 with the quotient as 4, giving the remainder = 7100 - 1544 × 4 = 7100 - 6176 = 924.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 6000.

Therefore, the square root of 6000 by long division method is 77.4 approx.

Is Square Root of 6000 Irrational?

The actual value of √6000 is undetermined. The value of √6000 up to 25 decimal places is 77.45966692414833770358531. Hence, the square root of 6000 is an irrational number.

☛ Also Check:

Square Root of 625 - √625 = 25
Square Root of 200 - √200 = 14.14214
Square Root of 63 - √63 = 7.93725
Square Root of 256 - √256 = 16
Square Root of 11 - √11 = 3.31662
Square Root of 149 - √149 = 12.20656
Square Root of 125 - √125 = 11.18034

Square Root of 6000 Solved Examples

Example 1: Solve the equation x² − 6000 = 0

Solution:

x² - 6000 = 0 i.e. x² = 6000
x = ±√6000
Since the value of the square root of 6000 is 77.460,
⇒ x = +√6000 or -√6000 = 77.460 or -77.460.
Example 2: If the area of a circle is 6000π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 6000π in²
⇒ r = ±√6000 in
Since radius can't be negative,
⇒ r = √6000
The square root of 6000 is 77.460.
⇒ r = 77.460 in
Example 3: If the area of a square is 6000 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 6000 in²
⇒ a = ±√6000 in
Since length can't be negative,
⇒ a = √6000 = 77.460 in

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FAQs on the Square Root of 6000

What is the Value of the Square Root of 6000?

The square root of 6000 is 77.45966.

Why is the Square Root of 6000 an Irrational Number?

Upon prime factorizing 6000 i.e. 2⁴ × 3¹ × 5³, 3 is in odd power. Therefore, the square root of 6000 is irrational.

Is the number 6000 a Perfect Square?

The prime factorization of 6000 = 2⁴ × 3¹ × 5³. Here, the prime factor 3 is not in the pair. Therefore, 6000 is not a perfect square.

What is the Value of 4 square root 6000?

The square root of 6000 is 77.460. Therefore, 4 √6000 = 4 × 77.460 = 309.839.

What is the Square Root of 6000 in Simplest Radical Form?

We need to express 6000 as the product of its prime factors i.e. 6000 = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 5. Therefore, √6000 = √2 × 2 × 2 × 2 × 3 × 5 × 5 × 5 = 20 √15. Thus, the square root of 6000 in the lowest radical form is 20 √15.

If the Square Root of 6000 is 77.460. Find the Value of the Square Root of 60.

Let us represent √60 in p/q form i.e. √(6000/100) = 60/10 = 7.746. Hence, the value of √60.0 = 7.746

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