ISEE Middle Level Math : How to find the square root

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

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Example Question #301 : Squares / Square Roots

Solve:

Possible Answers:

Correct answer:

Explanation:

  

because  

Example Question #301 : How To Find The Square Root

Solve:

Possible Answers:

Correct answer:

Explanation:

 indicates the negative square root of .

The square root of  because 

Because the negative sign is outside of the radical sign

 

 

Example Question #301 : Squares / Square Roots

Possible Answers:

Correct answer:

Explanation:

 

 

Example Question #302 : How To Find The Square Root

What is the  rounded to the nearest hundreth?

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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 #303 : How To Find The Square Root

Possible Answers:

Correct answer:

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 #304 : How To Find The Square Root

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

Possible Answers:

Correct answer:

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 #305 : How To Find The Square Root

Solve the equation:

Possible Answers:

Correct answer:

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 #306 : How To Find The Square Root

Determine the value of the square root:  

Possible Answers:

Correct answer:

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 .

The answer is:  

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