Question

# To multiply: The given expression. Then simplify if possible. Assume that all variables represent positive real numbers. Given: An expression: displaystylesqrt{{3}}{left(sqrt{{27}}-sqrt{{3}}right)}

To multiply:
The given expression. Then simplify if possible. Assume that all variables represent positive real numbers.
Given:
An expression: $$\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}$$

2020-11-24
Calculation:
To find the product of given expression, we will use distributive property
$$\displaystyle{a}{\left({b}+{c}\right)}={a}{b}+{a}{c}$$ as shown below:
$$\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}$$ (Given expression)
$$\displaystyle\Rightarrow\sqrt{{3}}\times\sqrt{{27}}-\sqrt{{3}}\times\sqrt{{3}}$$ (Using distributive property)
$$\displaystyle\Rightarrow\sqrt{{{3}\times{27}}}-\sqrt{{{3}\times{3}}}$$ (Applying rule root(n)a xx root(n)b = root(n)(ab))
$$\displaystyle\Rightarrow\sqrt{{81}}-\sqrt{{9}}$$
$$\displaystyle\Rightarrow\sqrt{{{9}^{2}}}-\sqrt{{{3}^{2}}}$$
$$\displaystyle\Rightarrow{9}-{3}\ \text{(Applying rule}\ \displaystyle{\sqrt[{{n}}]{{{a}^{n}}}}={a}$$)
$$\displaystyle\Rightarrow{6}$$
Therefore, the product of the given expressions would be 6.