Vertex is (-2,-3) and it's a minimum.
Q) Without a calculator, we must estimate the value of the following expression:
![3-\sqrt[]{38}.](https://tex.z-dn.net/?f=3-%5Csqrt%5B%5D%7B38%7D.)
A) I estimate 3 - √38 to be approximately -3.2.
First, we estimate the value of √38. √38 is between √36 and √49, but close to √36 (since 38 is closer to 4 than it is to 9). Since √36 is 6, √38 is probably something like 6.1 or 6.2. Filling 6.2 in the expression and simplifying, we have this:

So, I expect the number 3 - √38 to be close to -3.2.
Using a calculator we find that: 3 - √38 ≅ -3.16, which it is approximately the result that we found.
Answer
Without a calculator we find that 3 - √38 ≅ -3.2.
Answer:
Step-by-step explanation:
Sine is opposite divided by the hypotenuse.
sin(30) = 9/y
1/2 = 9/y
y = 18
Cosine is adjacent divided by the hypotenuse
cos(30) = x/18

Answer:
2√3
Step-by-step explanation:
So √12 is in radical form. I think what you are asking for is to reduce the expression to its **simplest** readical form.
So 12 = 4*3, √12 = √4 * √3.
So 12 = 4*3, √12 = √4 * √3.
We can ‘reduce’ this by noting that √4 =2, so the expression becomes 2√3.
This cannot be further reduced because 3 isn’t a square or divisible by a square, so 2√3 is the simplest radical form.
Answer: 12.2474487139
Step-by-step explanation:
(I think what you wrote is just the square root of 150? if I read this wrong please let me know so I can correct my answer.)
*If you plug in the square root of 150 into a calculator, you get 12.2474487139