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)}

Rational exponents and radicals
ANSWERED
asked 2020-11-23
To multiply:
The given expression. Then simplify if possible. Assume that all variables represent positive real numbers.
Given:
An expression: \(\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}\)

Expert Answers (1)

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.
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