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Square Root of 10000

The square root of 10000 is expressed as √10000 in the radical form and as (10000)^½ or (10000)^0.5 in the exponent form. The square root of 10000 is 100. It is the positive solution of the equation x² = 10000. The number 10000 is a perfect square.

Square Root of 10000: 100
Square Root of 10000 in exponential form: (10000)^½ or (10000)^0.5
Square Root of 10000 in radical form: √10000

1.	What is the Square Root of 10000?
2.	How to find the Square Root of 10000?
3.	Is the Square Root of 10000 Rational?
4.	FAQs

What is the Square Root of 10000?

The square root of 10000, (or root 10000), is the number which when multiplied by itself gives the product as 10000. Therefore, the square root of 10000 = √10000 = 100.

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How to Find Square Root of 10000?

Square Root of 10000 by Long Division Method

Value of √10000 by Long Division Method

Explanation:

Forming pairs: 01, 00 and 00
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
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 (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 0) such that 2Z × Z <= 0. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 0.
Divide 0 by 20 with the quotient as 0, giving the remainder = 0 - 20 × 0 = 0 - 0 = 0.
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 (0) to the divisor (20) i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 0) such that 20Z × Z <= 0. After finding Z, together 20 and Z (0) form a new divisor 200 for the new dividend 0.
Divide 0 by 200 with the quotient as 0, giving the remainder = 0 - 200 × 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 10000 by long division method is 100.

Is Square Root of 10000 Rational?

The value of √10000 is 100. Hence, the square root of 10000 is a rational number.

☛ Also Check:

Square Root of 120 - √120 = 10.95445
Square Root of 44 - √44 = 6.63325
Square Root of 63 - √63 = 7.93725
Square Root of 69 - √69 = 8.30662
Square Root of 74 - √74 = 8.60233
Square Root of 85 - √85 = 9.21954
Square Root of 200 - √200 = 14.14214

Square Root of 10000 Solved Examples

Example 1: Solve the equation x² − 10000 = 0

Solution:

x² - 10000 = 0 i.e. x² = 10000
x = ±√10000
Since the value of the square root of 10000 is 100,
⇒ x = +√10000 or -√10000 = 100 or -100.
Example 2: If the surface area of a cube is 60000 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 = 60000 in²
⇒ a = ±√10000 in
Since length can't be negative,
⇒ a = √10000
We know that the square root of 10000 is 100.
⇒ a = 100 in
Example 3: If the area of a circle is 10000π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 10000π in²
⇒ r = ±√10000 in
Since radius can't be negative,
⇒ r = √10000
Square root of 10000 is 100.
⇒ r = 100 in

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FAQs on the Square Root of 10000

What is the Value of the Square Root of 10000?

The square root of 10000 is 100.

Why is the Square Root of 10000 a Rational Number?

Upon prime factorizing 10000 i.e. 2⁴ × 5⁴, we find that all the prime factors are in even power. This implies that the square root of 10000 is a positive integer. Therefore, the square root of 10000 is rational.

If the Square Root of 10000 is 100. Find the Value of the Square Root of 100.

Let us represent √100 in p/q form i.e. √(10000/100) = 100/10 = 10. Hence, the value of √100 = 10

What is the Square of the Square Root of 10000?

The square of the square root of 10000 is the number 10000 itself i.e. (√10000)² = (10000)^2/2 = 10000.

Evaluate 14 plus 5 square root 10000

The given expression is 14 + 5 √10000. We know that the square root of 10000 is 100. Therefore, 14 + 5 √10000 = 14 + 5 × 100 = 14 + 500 = 514

Is the number 10000 a Perfect Square?

The prime factorization of 10000 = 2⁴ × 5⁴. Here, all the numbers are in the power of 2. This implies that the square root of 10000 is a positive integer. Therefore, 10000 is a perfect square.

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