Question

How do you simplify the square root of $18$ minus the square root $50?$

Answer 1

Hint: We will find the Mathematical words corresponding to each word in the given word phrase. We will replace the words with the corresponding Mathematical counterparts in the given statement. We will use the identity $\sqrt{ab}=\sqrt{a}\sqrt{b}.$

Complete step by step solution:
Let us consider the given word phrase, the square root of $18$ minus the square root of $50.$
Let us focus on the operation mentioned in the given statement, minus.
From this, we can understand that the operation takes place as subtraction.
That mean, the statement says that the square root of $50$ is subtracted from the square root of $18.$
We can write this as the square root of $18 -$ the square root of $50.$
We know that the square root of $18$ can be expressed Mathematically as $\sqrt{18}$ and the square root of $50$ can be represented Mathematically as $\sqrt{50}.$
So, we are going to replace the words with their counterparts. We know that it will not change the meaning of the given word phrase.
We will get $\sqrt{18}-\sqrt{50}.$
We know that $18=2\times 9$ and $50=2\times 25.$
So, if we apply them in the statement we have obtained, then we will get $\sqrt{2\times 9}-\sqrt{2\times 25}.$
Let us use the identity given by $\sqrt{ab}=\sqrt{a}\sqrt{b}.$
When we apply this identity in our problem, we will get $\sqrt{2}\sqrt{9}-\sqrt{2}\sqrt{25}.$
We know that $\sqrt{9}=\pm 3$ and $\sqrt{25}=\pm 5.$
So, we will get $\pm 3\sqrt{2}-\pm 5\sqrt{2}.$
We will get $\pm 3\sqrt{2}-\pm 5\sqrt{2}=\pm 2\sqrt{2},\pm 8\sqrt{2}.$
Hence the simplified form can be any of \[\pm 2\sqrt{2}, \pm 8\sqrt{2}.\]

Note: Even though this is a Mathematical statement, we should always remember that all physical situations can be interpreted Mathematically. If it is necessary, we can find the root values and we will get the values in the decimal forms but that can be a lengthy method so we prefered to stay with an easier one.