Question

Which is the simplificd form of \(33 \sqrt{\frac{2}{121}} ?\) (A) \(\frac{2 \sqrt{33}}{\sqrt{11}}\) (B) \(33 \sqrt{2}\) (C) \(3 \sqrt{2}\) (D) \(\frac{3 \sqrt{2}}{\sqrt{11}}\)

Short answer

The simplified form of the given expression is \(\frac{33 \sqrt{2}} {\sqrt{11}}\) (which is not in the options).

Step-by-step solution

Simplify the Fraction within the Square Root

Firstly, consider the fraction within the square root, \(\frac{2}{121}\). The square root of 121 is 11, hence the simplification results in \(\frac{2}{11}\). So the given expression after simplification jumps to: \(33\sqrt{\frac{2}{11}}\).

Separate the square root

To simplify further, separate the square root into two square root expressions, so it becomes \(33 \sqrt{2} \sqrt{\frac{1}{11}}\). This simplification is possible due to the property \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).

Simplify the second square root

Now, simplify \(\sqrt{\frac{1}{11}}\). The square root of any number 'a' is \(\frac{1}{\sqrt{a}}\). Therefore: \(\sqrt{\frac{1}{11}} = \frac{1}{\sqrt{11}}\).

Insert the simplified square root

Replace the value of \(\sqrt{\frac{1}{11}}\) in the expression. Now, the expression becomes \(33 \sqrt{2} \cdot \frac{1}{\sqrt{11}}\).

Solve the expression

Multiplying, we get the simplified answer as \(\frac{33 \sqrt{2}} {\sqrt{11}}\). So, the simplified form of the given expression is \(\frac{33 \sqrt{2}} {\sqrt{11}}\).