Question

What is the square root of $800$ simplified in radical form?

Answer 1

Hint: To simplify it, first we will find the square root of 800. We will find the factors of 800 and try to express them such that any of its factors turns out to be a perfect square. If we get a perfect square, we can easily find its square root by taking out the number from the square root and writing the factor once. For example if we have 4 written inside the square root, then we know that it can be expressed as $2 \times 2$ and so we get the square root of 4 as 2.

Complete step by step answer:
According to the question, we have to calculate the square root of \[800\] in radical form. The symbol \[\sqrt[n]{x}\] is known as the radical symbol. Simplifying in radical form in this question means that we have to calculate the square root of \[800\] in simplified form as it is clearly mentioned in the question that we have to find the square root of \[800\].
For calculating this, we will find the perfect squares of \[800\] and then write \[800\] in terms of their multiplication.
The factors of 800 which are perfect square are
\[1,\,4,\,16\,,\,25\,,\,100\,,400\]
For making it easy we will write 800 as multiplication of two numbers from which one will be its largest factor
\[800=400\times 2\]
Now use the radical symbol on both sides,
\[\sqrt{800}=\sqrt{400\times 2}\]
\[\sqrt{x\times y}\] can be written as \[\sqrt{x}\times \sqrt{y}\,\,\]
So, we can write the above equation in the same way,
\[\sqrt{800}=\sqrt{400}\times \sqrt{2}\]
AS we know, \[400\] is the perfect square of \[20\],
So, \[\sqrt{400}\] can be written as \[\,20\],
Substituting it in the above equation, we have
\[\sqrt{800}=20\times \sqrt{2}\]
\[\sqrt{800}=20\sqrt{2}\]

Therefore, the square root of \[800\] in radical form is \[20\sqrt{2}\].

Note: The radical sign \[\sqrt[n]{x}\] is read as \[x\] radical \[n\] or it can be said as the \[{{n}^{th}}\] root of \[x\]. In this symbol the quantity \[n\] is called the index. Square root and cube root can be said as the special case of radical form. The quantity written under the radical sign is known as radicand and the horizontal line under which the radicand is written is called vinculum.