Question

How do you simplify \[\sqrt{1008}\]?

Answer 1

Hint: From the question given, we have been asked to simplify \[\sqrt{1008}\]. We can clearly observe that the given number is in the form of square roots. In the case of square roots, if the number inside the square root is a perfect square, then the given question can be simplified very easily. If the number inside the square root is not a perfect square then we have another method to simplify it.

Complete step by step answer:
From the question, we had been given that \[\sqrt{1008}\].
We can clearly observe that the given number inside the square root is \[1008\].
We also know that \[1008\] is not a perfect square number.
If the number inside the square root is not a perfect square number then we have to follow the below method.
We have to split the radicals like \[\sqrt{{{a}^{2}}b}\].
First, we have to write the factor pairs of \[1008\], then we have to look for the biggest square number in the factor pairs.
Square numbers present for \[1008\] are \[9,16,36,144\].
As we have been already discussed above, we have to take the biggest square number.
We can clearly observe that \[144\] is the biggest square number.
Now, as of process,
\[\sqrt{1008}=\sqrt{144\left( 7 \right)}\]
\[\Rightarrow \sqrt{1008}=\sqrt{144}\sqrt{7}\]
\[\Rightarrow \sqrt{1008}=12\sqrt{7}\]
Hence \[\sqrt{1008}\] can be written simply as \[12\sqrt{7}\].
Hence simplified.

Note:
 We should be well aware of the radicals. We should be well aware of the splitting of radicals into products of numbers. Also, we should be very careful while doing the simplification. Also, we should be very careful when splitting the radicals, because the whole thing depends on it. It’s better for us to remember some squares and cubes. Similarly we can answer $\sqrt{256}=16$