4) $$ \begin{array}{l} ext { त्रA) Simplify } \ \sqrt{\frac{42}{75}} \ \end{array} $$ ?

Question

4) $$ \begin{array}{l}	ext { त्रA) Simplify } \ \sqrt{\frac{42}{75}} \ \end{array} $$ ?

UpStudy AI · Accepted Answer

To simplify $$ \sqrt{\frac{42}{75}} $$, follow these steps:

1. **Simplify the Fraction Inside the Square Root:**
   
   $$
   \frac{42}{75} = \frac{6 \times 7}{3 \times 25} = \frac{2 \times 7}{25} = \frac{14}{25}
   $$
   
   Here, the common factor of 3 in the numerator and denominator cancels out.

2. **Take the Square Root of the Simplified Fraction:**
   
   $$
   \sqrt{\frac{14}{25}} = \frac{\sqrt{14}}{\sqrt{25}} = \frac{\sqrt{14}}{5}
   $$
   
   Since $$ \sqrt{25} = 5 $$, the expression simplifies to $$ \frac{\sqrt{14}}{5} $$.

**Final Answer:**

$$
\frac{\sqrt{14}}{5}
$$
$$ \frac{\sqrt{14}}{5} $$

4) \( \begin{array}{l}\text { त्रA) Simplify } \\ \sqrt{\frac{42}{75}} \\ \end{array} \) ?

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