Question

How do you simplify $5$ times square root of $3$ plus $4$ times square root of $3?$

Answer 1

Hint: We will write the expression in Mathematical form. We will write the Mathematical counterpart of each term in the given statements. Then we will take common factors out. Later, we will add the summands.

Complete step by step solution:
Let us consider the given problem.
We are asked to show how we simplify the expression given by,
$5$ times square root of $3$ plus $4$ times square root of $3.$
Let us find the Mathematical form of the given expression.
For that, let us find the corresponding Mathematical counter parts of the given terms.
We know that by plus we mean the addition.
So, we can understand that there are two summands in the given expression. And they are $5$ times square root of $3$ and $4$ times square root of $3.$
That is, $5$ times square root of $3 + 4$ times square root of $3.$
Let us consider the summands of this expression.
In both of these summands, we can see a term times by which we mean the multiplication.
If we say that a number times another, we mean to say that we need to multiply these two numbers.
So, in the first summand, $5$ times square root of $3$ implies that we need to find the product of $5$ and the square root of $3.$
That is, $5 \times $ square root of $3.$
Similarly, in the second summand, $4$ times square root of $3$ implies the multiplication of $4$ and the square root of $3.$
That can be written as $4 \times $ square root of $3.$
We know that the square root of $3=\sqrt{3}$ lies in both the summands.
If we substitute $\sqrt{3}$ in the first summand, we will get $5\times \sqrt{3}=5\sqrt{3}$ and in the second summand, we will get $4\times \sqrt{3}=4\sqrt{3}.$
Now the expression will become $5\sqrt{3}+4\sqrt{3}.$
Now to simplify this expression we can take the common factor $\sqrt{3}$ out,
$\Rightarrow 5\sqrt{3}+4\sqrt{3}=\left( 5+4 \right)\sqrt{3}$
Now by usual addition, we will get $5\sqrt{3}+4\sqrt{3}=9\sqrt{3}.$
Hence, the simplified form of the given expression is $5\sqrt{3}+4\sqrt{3}=9\sqrt{3}.$

Note: The value of $\sqrt{3}=1.732.$ Therefore, you can further simplify the term $9\sqrt{3}$ as $9\sqrt{3}=9\times 1.732=15.59.$ On the other hand, we can write $9\sqrt{3}=\sqrt{{{9}^{2}}\times 3}=\sqrt{81\times 3}=\sqrt{243}.$ But you can leave $9\sqrt{3}$ as it is, if you are not asked for further simplification.