Add the following terms if possible: 5 times the square root of 50 plus 3 times the square root of 32.

Step-by-step solution

1. 1

   Notice the radicals do not match yet. $\sqrt{50}$ and $\sqrt{32}$ have different radicands, so they cannot be added as written. Simplifying first is what makes them alike.

2. 2

   Simplify the first radical. $50 = 25 \cdot 2$, so $\sqrt{50} = 5\sqrt{2}$ and the first term becomes $5 \cdot 5\sqrt{2} = 25\sqrt{2}$.

3. 3

   Simplify the second radical. $32 = 16 \cdot 2$, so $\sqrt{32} = 4\sqrt{2}$ and the second term becomes $3 \cdot 4\sqrt{2} = 12\sqrt{2}$.

4. 4

   Add the like radicals. Both terms now carry $\sqrt{2}$, so $25\sqrt{2} + 12\sqrt{2} = 37\sqrt{2}$.

5. 5

   Check numerically. $5\sqrt{50} \approx 35.35534$ and $3\sqrt{32} \approx 16.97056$; their sum is $\approx 52.32590$, and $37\sqrt{2} \approx 52.32590$.