Questions: -sqrtfrac5081

$-sqrtfrac5081$

Transcript text: \[ -\sqrt{\frac{50}{81}} \]

Solution

Solution Steps

Step 1: Simplify the fraction inside the square root

The expression is: \[ -\sqrt{\frac{50}{81}} \] First, simplify the fraction $\frac{50}{81}$. Since 50 and 81 have no common factors other than 1, the fraction is already in its simplest form.

Step 2: Break down the square root

Next, break down the square root into the square root of the numerator and the square root of the denominator: \[ -\sqrt{\frac{50}{81}} = -\frac{\sqrt{50}}{\sqrt{81}} \]

Step 3: Simplify the square roots

Simplify $\sqrt{50}$ and $\sqrt{81}$: \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \] \[ \sqrt{81} = 9 \]

Step 4: Substitute the simplified square roots back into the expression

Substitute the simplified square roots back into the expression: \[ -\frac{\sqrt{50}}{\sqrt{81}} = -\frac{5\sqrt{2}}{9} \]