Question

How do you simplify $3\sqrt{x}.3\sqrt{x}?$

Answer 1

Hint: Before starting to solve the given problem we know that here we have to simplify it. For that we have to apply the product theorem rule. We will also rearrange the equation while writing it a square for the given term because here we are multiplying one form times. The product rule we have $\Rightarrow {{\left( a\sqrt{x} \right)}^{2}}={{a}^{2}}\sqrt{{{x}^{2}}}$
After applying this rule we have to simplify it until we don't get the solution.

Complete step-by-step solution:
In the above numerical we have to simplify $3\sqrt{x}.3\sqrt{x}$
We can also rearrange the equation while writing it as a square for $3\sqrt{x}$ because here we are multiplying one form times. So, we can write it as follow ${{\left( 3\sqrt{x} \right)}^{2}}$
Now further solving the above equation we can introduce the theorem of product rule in the above equation we get as.
$\Rightarrow $${{3}^{2}}\sqrt{{{x}^{2}}}$
As we know when we are solving $3$ with its power of $2$ we get the value of $3$ into $3$ i.e. $3\times 3=9$
So, we can write further as,
$\Rightarrow $$9\sqrt{{{x}^{2}}}$
Here in the above equation we $9$ by solving ${{3}^{2}}$ but again we have $\sqrt{{{x}^{2}}}$ were its root and square we can also write it as $x.$
Formula as.
$\Rightarrow $$\sqrt[n]{{{a}^{x}}}={{a}^{\dfrac{x}{n}}}$
Here form above formula we can write
$\Rightarrow $$\sqrt{x}={{x}^{\dfrac{1}{2}}}$
Thus we get the equation further solving we have,
$\Rightarrow $$9{{\left( {{x}^{\dfrac{1}{2}}} \right)}^{2}}$
Now as we know here we have $\left( {{x}^{\dfrac{1}{2}}} \right)$ and the power of $2,$ so we are going to solve with power rule.
For the power of exponent we can also solve as below:
$\Rightarrow $${{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}}$
Thus we can write it as.
$\Rightarrow $$9{{x}^{\dfrac{1}{2}.2}}$
When we multiply the power $\dfrac{1}{2}$ with $2$ it cancels each other we get $1$ only.
So, we have $9{{x}^{1}}$
Here, the power of $1$ simplify
$\Rightarrow $$9x$

Hence when we simplify we get $9x.$

Note: There are various properties for finding the solutions. Various properties are applicable for the various types of problems. Such as \[{{x}^{a}}.\text{ }{{x}^{b}}={{x}^{a+b}}\] this is the property use for adding. Another property we have \[{{(xy)}^{a}}={{x}^{a}}{{y}^{a}}\] this property shows us multiplication with the same exponents. There is also the quotient property \[\dfrac{{{x}^{a}}}{{{x}^{b}}}={{x}^{a-b}}\] this property tells us about we have to divide the power with the same base we only just have to subtract the components.