Question

How do you solve ${{x}^{2}}=96$?

Answer 1

Hint: We can solve the above given question by using certain transformations. Perfect transformations should be used to get the perfect value. Transformations that have been made should be used to further simplify the given question.

Complete step by step answer:
From the question it had been given that, ${{x}^{2}}=96$
As we have been discussed above, we have to use some perfect transformations to solve the above given equation from the question.
We have to apply square root on both sides of the equation to get the equation solved.
By applying the square root on both sides of the given equation we get,
${{x}^{2}}=96$
$\Rightarrow \sqrt{{{x}^{2}}}=\sqrt{96}$
$\Rightarrow x=\sqrt{96}$
As $96$ is not a perfect square number, we do not get exact integer value for the given question.
So, the next step is seeing if we can simplify the radical.
We can simplify the radical by writing it as a product of two numbers.
We can write $96$ as the product of $16$ and $6$.
By writing $96$ as product of the numbers $16$ and $6$, we get
$x=\sqrt{16\times 6}$
We know that $16$ is a perfect square number.
Therefore $\sqrt{16}=4$
$\Rightarrow x=\sqrt{16}\times \sqrt{6}$
$\Rightarrow x=4\sqrt{6}$
Hence, the equation is simplified.

Note:
We should be well aware of the square roots and their simplification. We should be well known about the perfect square numbers. We should be well known about the perfect transformations that are made to the given question to get it solved. We should make sure that they have used the exact transformations or not. Calculation part also must be done very carefully by us. Similarly we can also solve ${{x}^{2}}=16\Rightarrow x=4$ .