To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 36 is 6, so the square root of 40 should be a little more than 6, around 6.32. 

Just like any other equation, isolate your variable. Start by multiplying both sides by :

Now, this is the same as:

You know that  is . You can intelligently rewrite this problem as:

, which is the same as:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

The square root of a number returns a positive and negative number that multiplies by itself to obtain the number inside the square root.

Simplifying the given equation gives us

Therefore, the correct answer is .

We are given the equation . To determine the value of , take the square root of both sides.

.

To calculate this value, take note of the following pattern:

Each succeeding radicand is  of the previous radicand, and the value of each succeeding square root is   of the previous value. Continuing the pattern:

. However, we are also given the condition that ; hence, we eliminate the extraneous solution  and conclude that the only valid solution of  is .

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative.  If the decimal had moved left, we would have had a positive exponent.  

In this case we get 6.009 * 10^–5.

We need to convert  into a number of the form .

The trick is, however, figuring out what  should be. When you have to move your decimal point to the right, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move to the left. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is:

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to .

For each of the answer choices, this would give us:

 (Which is, thus, the answer.)

When you convert, you add for each place that you move to the left and subtract for each place you move to the right. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point four places to the right. Since the number is less than zero, the exponent is negative: