Questions: Find -√(100/9)

Transcript text: Find $-\sqrt{\frac{100}{9}}$

Solution

Solution Steps

Step 1: Simplify the fraction inside the square root

The expression is $-\sqrt{\frac{100}{9}}$. First, simplify the fraction $\frac{100}{9}$. Since both 100 and 9 are perfect squares, this fraction can be simplified as follows: \[ \frac{100}{9} = \left(\frac{10}{3}\right)^2 \]

Step 2: Take the square root of the simplified fraction

Now, take the square root of $\left(\frac{10}{3}\right)^2$: \[ \sqrt{\left(\frac{10}{3}\right)^2} = \frac{10}{3} \]

Step 3: Apply the negative sign

Finally, apply the negative sign outside the square root: \[ -\sqrt{\frac{100}{9}} = -\frac{10}{3} \]

The answer is $-\frac{10}{3}$, so the correct choice is A.

Final Answer

$\boxed{-\frac{10}{3}}$

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