# ACT Math : Squaring / Square Roots / Radicals

## Example Questions

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### Example Question #1 : Squaring / Square Roots / Radicals

can be rewritten as:

Explanation:

Use the formula for solving the square of a difference, . In this case,

### Example Question #2 : Squaring / Square Roots / Radicals

Expand:

Explanation:

To multiply a difference squared, square the first term and add two times the multiplication of the two terms. Then add the second term squared.

### Example Question #3 : Squaring / Square Roots / Radicals

The expression   is equivalent to:

Explanation:

First, we need to factor the numerator and denominator separately and cancel out similar terms. We will start with the numerator because it can be factored easily as the difference of two squares.

Now factor the quadratic in the denominator.

Substitute these factorizations back into the original expression.

The  terms cancel out, leaving us with the following answer:

### Example Question #4 : Squaring / Square Roots / Radicals

Evaluate the following expression:

Explanation:

2 raised to the power of 5 is the same as multiplying 2 by itself 5 times so:

25 = 2x2x2x2x2 = 32

Then, 5x2 must first be multiplied before taking the exponent, yielding 102 = 100.

100 + 32 = 132

### Example Question #5 : Squaring / Square Roots / Radicals

Expand:

Explanation:

To multiply a difference squared, square the first term and add two times the multiplication of the two terms. Then add the second term squared.

### Example Question #6 : Squaring / Square Roots / Radicals

Which of the following is the square of  ?

Explanation:

Use the square of a sum pattern, substituting  for  and  for  in the pattern:

### Example Question #7 : Squaring / Square Roots / Radicals

Which of the following is the square of  ?

You may assume both  and  are positive.

Explanation:

Use the square of a sum pattern, substituting  for  and  for  in the pattern:

or

### Example Question #8 : Squaring / Square Roots / Radicals

Which of the following is the square of  ?

Explanation:

Multiply vertically as follows:

### Example Question #9 : Squaring / Square Roots / Radicals

Which of the following is the square of   ?

The correct answer is not given among the other responses.

The correct answer is not given among the other responses.

Explanation:

Use the square of a sum pattern, substituting  for  and  for  in the pattern:

This is not equivalent to any of the given choices.

### Example Question #10 : Squaring / Square Roots / Radicals

Which of the following is the square of  ?