Roots in Expressions

A root is worked out before the products and sums around it, just as a power is. In $3\cdot \sqrt{25}+2$ the root goes first: $\sqrt{25}$ is 5, so the line becomes $3\cdot 5+2$. Then the multiplication, $15+2$, and last the sum, 17.

Notice how the board writes $3\cdot \sqrt{25}$: the 3 sits right against the root sign with no dot, the same way 3(2 + 4) meant 3 times the package. It means 3 times $\sqrt{25}$. It is not the third root of 25, which would have a small raised 3 tucked into the sign, and the 3 does not go under the sign either.

Why the root first? The 3 is waiting to multiply a number, and until you take the root, you do not know which number that is. The root sign works like a package around 25 that must be opened before it can be used.