But the radical sign implies the principal root.

We're taking the principal root, the positive square root.

The square root of 16 times 2 is the square root of 16 times the square root of 2.

So the square root of 12 is equal to square root of 3 times square root of 4.

The square root of 2 times the square root of x.

Square root of 4 over square root of 9, times x.

Times the square root of 5 times the square root of s.

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So square root of 2 times 2 times the square root of 5 times the square root of 9.

So we take the square root of both sides, you get I is equal to the square root of 3 over the square root of 4.

AND BE CAREFUL HERE, IF WE JUST TAKE THE PRlNClPLE ROOT, THE PRlNClPLE ROOT HERE IS THE POSlTIVE SQUARE ROOT

Times the square root of three, times the square root of three

Square root of three times square root of three

So b is equal to 36 minus 20 is 16. So square root of 16 over square root of 5.

It's going to be the square root of this times square root of that.

Square root of 12 is the same thing as the square root of 3 times the square root of 4.

The principal square root of 4 is 2, so this all simplifies and we can switch the order over here this is equal to 2 times the square root of 13 2 times the principal square root of 13, I should say, times i.

And this is just going to be equal to the principal root of 5x.

We are looking for the principle root of this is the same thing, this is the same thing as d times the principle root of 4 times the principle root of d to the fourth, times the principle root of d to the fourth

It's going to be 2 times the square root of 5 minus the square root of 5 times the square root of 5, which is 5.

And so this the same thing as the square root of 4 times 4 times the square root of 5 times 5 times the square root of 5.

But if you just write a radical sign, you're actually referring to the positive square root, or the principal square root.

Which is the same thing as the cube root, which is the same thing as the cube root of 1 times the cube root of 512 and this one is pretty straight forward to answer.

Times the principle root of 5 times the principle root, times the principle root of x squared times the principle root of x.

The square root of 9 times 9, the square root of 81.

So w is going to be equal to the square root of 25, the positive square root.

Well the square root of 2 times the square root of 2 is 2.

And the radical sign doesn't just have to apply to a square root.

This is the square root of 2 times the square root of 3.

Of thirty two divided by the cube no, I'll just take the square root.

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The positive square root.

learned before that's actually the principal square root of 8, or the positive square root of 8 minus 6 times the principal square root of 32.

And then they would tell you that, Hey, look, just from straight up properties of the principal square root function, they'll tell you the square root of a times b is the same thing as the principal square root of a, times the principal square root of b.

So you could view this as square root of 2 minus the square root of 6, or the principal square root of 2 minus the principal square root of 6, x squared.

It could be the principle root, or it could be the negative root.

And then this over here is minus the principle square root of x squared, times the principle square root of x.