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# What is the square root of $200$ ?

Last updated date: 13th Jul 2024
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Hint: Square Root: A square root of a number is a value that can be multiplied by itself to give the original number. It is a function of $y = \sqrt x$ . The principal square root is the positive number square root. Unless “the square root of a number refers only to the principal square root. The square root is usually denoted as $'\sqrt {} '$ and it is known as a radical symbol.

Complete step by step solution:
Given,
First of all we have to factorize the number $200$ ,
$\Rightarrow 200 = 2 \times 2 \times 2 \times 5 \times 5$
Now we have to make the set and take out the radical.
The square root of given number is,
$= \sqrt {200}$
by factrosing it,
$= \sqrt {25 \times 8}$
$= \sqrt {5 \times 5 \times 2 \times 2 \times 2}$
Now make the set and take out from the radical.
$= 5 \times 2\sqrt 2$
$= 10\sqrt 2$
So, the correct answer is “ $10\sqrt 2$ ”.

Note: The square root property is the one method to solve the quadratic equations. The method is generally used in equations that have the form $a{x^2} = c$ or ${(ax + b)^2} = c$ the equation which can be expressed on either of those forms. We can take square roots from both sides. The square root of a negative number is known as a complex number.