Question

Combine the following expressions.

Answer 1

Answer:

second option

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Simplifying the radicals

$\sqrt{27x^{3} }$

= $\sqrt{9(3)x^2.x}$

= $\sqrt{9}$ × $\sqrt{3}$ × $\sqrt{x^2}$ × $\sqrt{x}$

= 3 × $\sqrt{3}$ × x × $\sqrt{x}$

= 3x$\sqrt{3x}$

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$\sqrt{12x^{3} }$

= $\sqrt{4(3)x^2.x}$

= $\sqrt{4}$ × $\sqrt{3}$ × $\sqrt{x^2}$ × $\sqrt{x}$

= 2 × $\sqrt{3}$ × x × $\sqrt{x}$

= 2x$\sqrt{3x}$

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Thus

3 × 3x$\sqrt{3x}$ - 2 × 2x$\sqrt{3x}$

= 9x$\sqrt{3x}$ - 4x$\sqrt{3x}$

= 5x$\sqrt{3x}$