Questions: Simplify. 3 √98 + 11 √2 - √50

Transcript text: Makayla Johnson: M ALEKS - Makayla Johnson - Rev - www-awy.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkasNW8D8A9PVVf Padicals Square root addition or sublinaction with three terms Simplify. \[ 3 \sqrt{98}+11 \sqrt{2}-\sqrt{50} \] $\square$ Explanation Crieck

Solution

Solution Steps

To simplify the expression $3 \sqrt{98} + 11 \sqrt{2} - \sqrt{50}$, we need to simplify each square root term by factoring out perfect squares. After simplifying, we combine like terms if possible.

Step 1: Simplifying Each Term

We start with the expression $3 \sqrt{98} + 11 \sqrt{2} - \sqrt{50}$. We simplify each square root term:

$ \sqrt{98} = \sqrt{49 \cdot 2} = 7 \sqrt{2} $
$ \sqrt{50} = \sqrt{25 \cdot 2} = 5 \sqrt{2} $

Thus, we can rewrite the expression as: \[ 3 \sqrt{98} = 3 \cdot 7 \sqrt{2} = 21 \sqrt{2} \] So the expression becomes: \[ 21 \sqrt{2} + 11 \sqrt{2} - 5 \sqrt{2} \]

Step 2: Combining Like Terms

Next, we combine the like terms: \[ (21 + 11 - 5) \sqrt{2} = 27 \sqrt{2} \]

Step 3: Calculating the Numerical Value

Now, we calculate the numerical value of $27 \sqrt{2}$: \[ \sqrt{2} \approx 1.4142 \quad \Rightarrow \quad 27 \sqrt{2} \approx 27 \cdot 1.4142 \approx 38.1838 \]