Square Root of 10000

The square root of 10000 is 100. This means when we multiply 100 twice with itself, the answer is 10000. Thus, The square of 100 is 10000, and the square root of 10000 is ±100. Mathematically, the square of 10000 is written as √10000 where the symbol ‘√’ is called the radical sign that denotes the square root of a number. In exponential form, the square root of 10000 is written as (10000)^½.

What is Square Root of 10000?

The square root of 10000 is a number that is when squared, gives the result 10000. Since both 100 and –100 when squared, gives the answer 10000. Therefore square root of 10000 is both 100 and –100.

How to Find the Square Root of 10000?

The prime factorisation method can easily determine the square root of 10000. It can be also determined by the repeated subtraction method and the long division method.

Prime Factorisation Method

To find the square root of 10000 by the prime factorisation method, we first prime factorise 10000 and then make pairs of two to get the square root.

Prime factorisation of 10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

Square root of 10000 = √[2 × 2 × 2 × 2 × 5 × 5 × 5 × 5] = 2 × 2 × 5 × 5 = 100

Long Division Method

To find the square root of 10000 by long division method, we shall write 10000 dividend and pair its digits from right to left. Thus, the square root of 10000 can be calculated as follows:

To learn how to find the square root of any number long division method, click here.

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Solved Examples on Square Root of 10000

Example 1:

The area of a square plot is 10000 m². Calculate the perimeter of the plot.

Solution:

Let a be the length of the square plot.

The area of the square plot = a² = 10000 m²

⇒ a = √10000 = 100 m (taking positive root since the length cannot be negative)

∴ the perimeter of the square plot = 4 × 100 = 400 m

Example 2:

Find the smallest number that must be added to 9985 so that it will be a perfect square number. Also, find the square root of that perfect square number.

Solution:

Given, 9985, we have to find the smallest number, which is then added to this, resulting in a square number.

Now, 99² = 9801 < 9985 < 10000 = 10²

Then, 10000 – 9985 = 15

Thus, 15 is the smallest number that must be added to 9985, 9985 + 15 = 10000 is the perfect square number.

Square root of 10000 = √10000 = 100.

Example 3:

Find the smallest number that must be multiplied with 1000 to be a perfect square number. Also, find the square root of that perfect square number.

Solution:

The prime factorisation of 1000 = 2 × 2 × 2 × 5 × 5 × 5.

To make it a perfect square, we have to multiply 2 × 5 = 10.

∴ the perfect square number = 1000 × 10 = 10000

Square root of 10000 = √[2 × 2 × 2 × 2 × 5 × 5 × 5 × 5] = 2 × 2 × 5 × 5 = 100.