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Square Root of 8100

The square root of 8100 is expressed as √8100 in the radical form and as (8100)^½ or (8100)^0.5 in the exponent form. The square root of 8100 is 90. It is the positive solution of the equation x² = 8100. The number 8100 is a perfect square.

Square Root of 8100: 90
Square Root of 8100 in exponential form: (8100)^½ or (8100)^0.5
Square Root of 8100 in radical form: √8100

Square Root of 8100

1.	What is the Square Root of 8100?
2.	How to find the Square Root of 8100?
3.	Is the Square Root of 8100 Rational?
4.	FAQs

What is the Square Root of 8100?

The square root of 8100, (or root 8100), is the number which when multiplied by itself gives the product as 8100. Therefore, the square root of 8100 = √8100 = 90.

☛ Check: Square Root Calculator

How to Find Square Root of 8100?

Square Root of 8100 by Long Division Method

Value of √8100 by Long Division Method

Explanation:

Forming pairs: 81 and 00
Find a number Y (9) such that whose square is <= 81. Now divide 81 by 9 with quotient as 9.
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 (9) to the divisor (9) i.e. 9 + 9 = 18. To the right of 18, find a digit Z (which is 0) such that 18Z × Z <= 0. After finding Z, together 18 and Z (0) form a new divisor 180 for the new dividend 0.
Divide 0 by 180 with the quotient as 0, giving the remainder = 0 - 180 × 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 8100 by long division method is 90.

Is Square Root of 8100 Rational?

The value of √8100 is 90. Hence, the square root of 8100 is a rational number.

☛ Also Check:

Square Root of 68 - √68 = 8.24621
Square Root of 125 - √125 = 11.18034
Square Root of 89 - √89 = 9.43398
Square Root of 1024 - √1024 = 32
Square Root of 80 - √80 = 8.94427
Square Root of 54 - √54 = 7.34847
Square Root of 105 - √105 = 10.24695

Square Root of 8100 Solved Examples

Example 1: Solve the equation x² − 8100 = 0

Solution:

x² - 8100 = 0 i.e. x² = 8100
x = ±√8100
Since the value of the square root of 8100 is 90,
⇒ x = +√8100 or -√8100 = 90 or -90.
Example 2: If the area of a circle is 8100π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 8100π in²
⇒ r = ±√8100 in
Since radius can't be negative,
⇒ r = √8100
Square root of 8100 is 90.
⇒ r = 90 in
Example 3: If the surface area of a cube is 48600 in². 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 = 6a² = 48600 in²
⇒ a = ±√8100 in
Since length can't be negative,
⇒ a = √8100
We know that the square root of 8100 is 90.
⇒ a = 90 in

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FAQs on the Square Root of 8100

What is the Value of the Square Root of 8100?

The square root of 8100 is 90.

Why is the Square Root of 8100 a Rational Number?

Upon prime factorizing 8100 i.e. 2² × 3⁴ × 5², we find that all the prime factors are in even power. This implies that the square root of 8100 is a positive integer. Therefore, the square root of 8100 is rational.

What is the Value of 2 square root 8100?

The square root of 8100 is 90. Therefore, 2 √8100 = 2 × 90 = 180.

Evaluate 4 plus 16 square root 8100

The given expression is 4 + 16 √8100. We know that the square root of 8100 is 90. Therefore, 4 + 16 √8100 = 4 + 16 × 90 = 4 + 1440 = 1444

What is the Square Root of -8100?

The square root of -8100 is an imaginary number. It can be written as √-8100 = √-1 × √8100 = i √8100 = 90i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 8100 is 90. Find the Value of the Square Root of 81.

Let us represent √81 in p/q form i.e. √(8100/100) = 81/10 = 9. Hence, the value of √81 = 9

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