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Square Root of 9999

The square root of 9999 is expressed as √9999 in the radical form and as (9999)^½ or (9999)^0.5 in the exponent form. The square root of 9999 rounded up to 6 decimal places is 99.995000. It is the positive solution of the equation x² = 9999. We can express the square root of 9999 in its lowest radical form as 3 √1111.

Square Root of 9999: 99.99499987499375
Square Root of 9999 in exponential form: (9999)^½ or (9999)^0.5
Square Root of 9999 in radical form: √9999 or 3 √1111

Square Root of 9999

1.	What is the Square Root of 9999?
2.	How to find the Square Root of 9999?
3.	Is the Square Root of 9999 Irrational?
4.	FAQs

What is the Square Root of 9999?

The square root of 9999, (or root 9999), is the number which when multiplied by itself gives the product as 9999. Therefore, the square root of 9999 = √9999 = 3 √1111 = 99.99499987499375.

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How to Find Square Root of 9999?

Square Root of 9999 by Long Division Method

Value of √9999 by Long Division Method

Explanation:

Forming pairs: 99 and 99
Find a number Y (9) such that whose square is <= 99. Now divide 99 by 9 with quotient as 9.
Bring down the next pair 99, to the right of the remainder 18. The new dividend is now 1899.
Add the last digit of the quotient (9) to the divisor (9) i.e. 9 + 9 = 18. To the right of 18, find a digit Z (which is 9) such that 18Z × Z <= 1899. After finding Z, together 18 and Z (9) form a new divisor 189 for the new dividend 1899.
Divide 1899 by 189 with the quotient as 9, giving the remainder = 1899 - 189 × 9 = 1899 - 1701 = 198.
Now, let's find the decimal places after the quotient 99.
Bring down 00 to the right of this remainder 198. The new dividend is now 19800.
Add the last digit of quotient to divisor i.e. 9 + 189 = 198. To the right of 198, find a digit Z (which is 9) such that 198Z × Z <= 19800. Together they form a new divisor (1989) for the new dividend (19800).
Divide 19800 by 1989 with the quotient as 9, giving the remainder = 19800 - 1989 × 9 = 19800 - 17901 = 1899.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 9999.

Therefore, the square root of 9999 by long division method is 99.9 approximately.

Is Square Root of 9999 Irrational?

The actual value of √9999 is undetermined. The value of √9999 up to 25 decimal places is 99.99499987499374960934765. Hence, the square root of 9999 is an irrational number.

☛ Also Check:

Square Root of 40 - √40 = 6.32456
Square Root of 1521 - √1521 = 39
Square Root of 39 - √39 = 6.24500
Square Root of 97 - √97 = 9.84886
Square Root of 76 - √76 = 8.71780
Square Root of 27 - √27 = 5.19615
Square Root of 51 - √51 = 7.14143

Square Root of 9999 Solved Examples

Example 1: Solve the equation x² − 9999 = 0

Solution:

x² - 9999 = 0 i.e. x² = 9999
x = ±√9999
Since the value of the square root of 9999 is 99.995,
⇒ x = +√9999 or -√9999 = 99.995 or -99.995.
Example 2: If the area of an equilateral triangle is 9999√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 = 9999√3 in²
⇒ a = ±√39996 in
Since length can't be negative,
⇒ a = √39996 = 2 √9999
We know that the square root of 9999 is 99.995.
⇒ a = 199.990 in
Example 3: If the surface area of a sphere is 39996π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 39996π in²
⇒ r = ±√9999 in
Since radius can't be negative,
⇒ r = √9999
The square root of 9999 is 99.995.
⇒ r = 99.995 in

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FAQs on the Square Root of 9999

What is the Value of the Square Root of 9999?

The square root of 9999 is 99.99499.

Why is the Square Root of 9999 an Irrational Number?

Upon prime factorizing 9999 i.e. 3² × 11¹ × 101¹, 11 is in odd power. Therefore, the square root of 9999 is irrational.

Is the number 9999 a Perfect Square?

The prime factorization of 9999 = 3² × 11¹ × 101¹. Here, the prime factor 11 is not in the pair. Therefore, 9999 is not a perfect square.

What is the Square Root of -9999?

The square root of -9999 is an imaginary number. It can be written as √-9999 = √-1 × √9999 = i √9999 = 99.994i
where i = √-1 and it is called the imaginary unit.

Evaluate 3 plus 16 square root 9999

The given expression is 3 + 16 √9999. We know that the square root of 9999 is 99.995. Therefore, 3 + 16 √9999 = 3 + 16 × 99.995 = 3 + 1599.920 = 1602.920

What is the Value of 2 square root 9999?

The square root of 9999 is 99.995. Therefore, 2 √9999 = 2 × 99.995 = 199.990.

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