Question

How do you simplify 9 square root 125?

Answer 1

Hint: The question says to simplify the $9\sqrt{125}$. This $\sqrt{{}}$ symbol tells us to find the square root of a particular number. A radical means square root. Basically, it can be any root. It can be a square root or may be a cube root also. Some important components you need to know about the radical are degree, radicand and radicand symbol.

Complete step by step answer:
Now, let’s solve the question.
Solving radicals is not a difficult task. All we need to know is what is radical and some of the important terms used in solving radicals.
Radical is nothing but an expression that contains a root, usually a square root or cube root. There are three main important components of radical. These are: degree, radicand and radicand symbol. If you want to know about radicand symbols, it means the ‘root of’ i.e. $\sqrt{{}}$. The expression needs to be solved first before removing the symbol. And degree actually indicates how many times a radicand is multiplied by itself. Apart from this, radicand is a term which refers to a number of which we have to find the root. For example: In $\sqrt{5x}$, 5x is a radicand.
Now, let us see the rule for radicals:
$\Rightarrow \sqrt{a}\times \sqrt{a}=\sqrt{a\times a}=\sqrt{{{a}^{2}}}=a$
As per question, we have:
$\Rightarrow 9\sqrt{125}$
Here, 125 is converted into its factors which can be further rooted. Basically we have to separate the factors which can be rooted and those which cannot be rooted. Let me show how it can be done.
$\Rightarrow 9\sqrt{25\times 5}$
We can further find the square root of 25 but not for 5. On solving further, 5 as the under root of 25 can be taken out.
$\Rightarrow 9\times 5\sqrt{5}$
Now, perform the required multiplication:
$\Rightarrow 45\sqrt{5}$
If you wish, you can put the value of $\sqrt{5}$ which is equal to 2.2360.
$\Rightarrow 45\times 2.2360$
$\therefore 9\sqrt{125}=100.62$
This is the final answer.

Note:
There is an alternative method to solve this question. We can use the decimal form too. Use a calculator to find the root of 125 which comes out to be 11.18 and then multiply 11.18 with 9 which comes out to be 100.62. The answer will be the same by both radical and decimal forms. All you need to know is the square and square roots.