# ISEE Middle Level Math : How to find the square root

## Example Questions

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Solve:

Explanation:

because

### Example Question #302 : Squares / Square Roots

Solve:

Explanation:

indicates the negative square root of .

The square root of  because

Because the negative sign is outside of the radical sign

Explanation:

### Example Question #304 : Squares / Square Roots

What is the  rounded to the nearest hundreth?

Explanation:

To find the ,  find the two perfect squares that this is between.

and the  would be the two perfect squares. Recall that square roots come from either two positive values multiplied together or two negative numbers are multiplied together. Thus two separate equations will need to be used to calculate the possible value of  .

Let's first take a look at the perfect square which surround .

In this particular case  would be closer to the  then the  because 10 is closer to 9 thus the appropriate estimation would be,

.

### Example Question #305 : Squares / Square Roots

Estimate  to the nearest whole integer.

Explanation:

Take the square root of both sides of the equation.

The first perfect square that is less than  is

The first perfect square that is greater than  is

The  ls between  and

is closer to  than .

For the equation      there are 2 solutions, because  is positive: , which is positive, and , which is negative. Together, these two roots are denoted .

or

is the correct answer.

### Example Question #306 : Squares / Square Roots

Explanation:

because .

because

The negative sign outside the radical sign indicates that you are taking the negative square root of what is inside the radical sign, or the radicand.

is the correct answer.

### Example Question #307 : Squares / Square Roots

If the area of a pasture is , and the pasture is a square, what is the length of one side of the pasture?

Explanation:

The area of a square is the side length squared. To find the side length of the square, find the

or what number times itself gives  as the product.

because

The correct answer is   ft.

### Example Question #308 : Squares / Square Roots

Solve the equation:

Explanation:

Take the square root of both sides of the equation:

For the equation      there are 2 solutions, because it is positive: , which is positive, and , which is negative. Together, these two roots are denoted .

### Example Question #309 : Squares / Square Roots

Determine the value of the square root:

Explanation:

The square root of a number determines one number that multiplies by itself to get the number inside the square root.

Notice that the number in the radical ends with a 9.  This means the ones digit of the final answer must be three.

The answers  and  cannot be true since:

Those values are far too small to be the correct answer.

The only possible answer is .