Chapter 9.9, Problem 10MRE

To determine

To simplify the expression $\sqrt{\frac{27x^4}{4}}$

Answer to Problem 10MRE

The simplified expression is $\frac{3\sqrt{3}{x}^2}{2}$ .

Explanation of Solution

Given: Expression: $\sqrt{\frac{27x^4}{4}}$

Calculation:

Given: Expression: $\sqrt{\frac{27x^4}{4}}$

The above expression can be written as:

  $\sqrt{\frac{(3^2\times 3)x^{(2\times 2)}}{(2\times 2)}}$

Whenever a square root of a number/fraction is taken, there are both positive and negative outcomes, since both the results when squared gives the same number/fraction.

Hence, taking the square root of the above expression, the result comes as:

  $\frac{3\sqrt{3}{x}^2}{2}$

Hence, the answer is -

  $\frac{3\sqrt{3}{x}^2}{2}$

Conclusion:

Hence, the solution is $\frac{3\sqrt{3}{x}^2}{2}$ .