How to find the square root - SSAT Middle Level Quantitative

For the square root of a number to fall between 18 and 19, the number has to fall between the squares of these numbers - that is:

If , then , or, equivalently,

All four choices fall in this range.

Find the individual square roots and perform the operations on them.

By definition, the square root of a number multiplied by itself yields that number. Therefore, 43 is the square root of .

By definition, the square root of a number multiplied by itself yields that number. Therefore,

.

First, find the square root of each number:

Then, solve the equation accordingly.

The answer is

The square root of a number is the number which, when multiplied by itself, yields that number. Since , .

The square root of a number is the number which, when multiplied by itself, yields that number. Since , .

The square root of a number is the number which, when multiplied by itself, yields that number. Since , .

The square root of a number is the number which, when multiplied by itself, yields that number. Since , , and

then

The two sides of the square must be the same length, and multiply to give 16. So we are looking for the which is .

A negative number does not have a real square root, so this is the correct choice.

, so .

, so .

Since ,

, so

can also be written as , so can also be written as , or .

Recognize that . Since , we can move the outside of the radical sign. This leaves us with .

The square root of is , since .

To find the square root of a fraction, extract the square root of both the numerator and the denominator. Since , , and since , .

Combine these results:

, so

.

The square root of a fraction can be determined by taking the square roots of both numerator and denominator. Since , , and since , . Therefore,

.