How to find the square of an integer Flashcards - ACT Math

Question

Solve: 3³

Answer

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

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Question

If (x - 3)2 = 64, what is a possible value of x?

Answer

In order to solve for x, we must first take the square root of both sides.

(x - 3)2 = 64

(x - 3) = +/- 8

The square root of 64 is either 8 or -8. We then solve the equation with both possible values of the square root of 64.

x - 3 = 8 (Add 3 to both sides.)

x = 11

x - 3 = -8 (Add 3 to both sides.)

x = -5

x = 11 or -5. -5 is the only possible value of x that is an answer choice.

Compare your answer with the correct one above

Question

When you square the following numbers, which one results in an irrational number?

Answer

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

Compare your answer with the correct one above

Question

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

Answer

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

Compare your answer with the correct one above

Question

$\dpi{100} \small \sqrt{15}$ is between what two integers?

Answer

$\dpi{100} \small 3\times 3=9$

$\dpi{100} \small 4\times 4=16$

falls between and

Therefore, $\dpi{100} \small \sqrt{15}$ is between and

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Question

Simplify the following: $8^{2}$

Answer

$8^{2}$ is the same as multiplied by . Thus, the answer is .

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Question

The last two digits in the square of a number have a product of . Which of the following could NOT be the last digit of ?

Answer

If the last two digits of the squared number multiply to , then the digits must be factors of . The last digit of any square of a number ending in will be , which is not a factor of . Thus, the number cannot end in .

Compare your answer with the correct one above

Question

Solve: 3³

Answer

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

Compare your answer with the correct one above

Question

If (x - 3)2 = 64, what is a possible value of x?

Answer

In order to solve for x, we must first take the square root of both sides.

(x - 3)2 = 64

(x - 3) = +/- 8

The square root of 64 is either 8 or -8. We then solve the equation with both possible values of the square root of 64.

x - 3 = 8 (Add 3 to both sides.)

x = 11

x - 3 = -8 (Add 3 to both sides.)

x = -5

x = 11 or -5. -5 is the only possible value of x that is an answer choice.

Compare your answer with the correct one above

Question

When you square the following numbers, which one results in an irrational number?

Answer

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

Compare your answer with the correct one above

Question

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

Answer

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

Compare your answer with the correct one above

Question

$\dpi{100} \small \sqrt{15}$ is between what two integers?

Answer

$\dpi{100} \small 3\times 3=9$

$\dpi{100} \small 4\times 4=16$

falls between and

Therefore, $\dpi{100} \small \sqrt{15}$ is between and

Compare your answer with the correct one above

Question

Simplify the following: $8^{2}$

Answer

$8^{2}$ is the same as multiplied by . Thus, the answer is .

Compare your answer with the correct one above

Question

The last two digits in the square of a number have a product of . Which of the following could NOT be the last digit of ?

Answer

If the last two digits of the squared number multiply to , then the digits must be factors of . The last digit of any square of a number ending in will be , which is not a factor of . Thus, the number cannot end in .

Compare your answer with the correct one above

Question

Solve: 3³

Answer

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

Compare your answer with the correct one above

Question

If (x - 3)2 = 64, what is a possible value of x?

Answer

In order to solve for x, we must first take the square root of both sides.

(x - 3)2 = 64

(x - 3) = +/- 8

The square root of 64 is either 8 or -8. We then solve the equation with both possible values of the square root of 64.

x - 3 = 8 (Add 3 to both sides.)

x = 11

x - 3 = -8 (Add 3 to both sides.)

x = -5

x = 11 or -5. -5 is the only possible value of x that is an answer choice.

Compare your answer with the correct one above

Question

When you square the following numbers, which one results in an irrational number?

Answer

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

Compare your answer with the correct one above

Question

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

Answer

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

Compare your answer with the correct one above

Question

$\dpi{100} \small \sqrt{15}$ is between what two integers?

Answer

$\dpi{100} \small 3\times 3=9$

$\dpi{100} \small 4\times 4=16$

falls between and

Therefore, $\dpi{100} \small \sqrt{15}$ is between and

Compare your answer with the correct one above

Question

Simplify the following: $8^{2}$

Answer

$8^{2}$ is the same as multiplied by . Thus, the answer is .

Compare your answer with the correct one above

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How to find the square of an integer - ACT Math

Solve: 3³

When using a cube root. 3³ becomes 3 * 3 * 3. 3 * 3 = 9 9 * 3 = 27

If (x - 3)2 = 64, what is a possible value of x?

When you square the following numbers, which one results in an irrational number?

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

The square of –2 is 4, of –3 is 9, and of 4 is 16. The sum of these squares is 29. The sum of (–2) + (–3) + (4) is –1. 29 – (–1) = 30

is between what two integers?

falls between and Therefore, is between and

Simplify the following:

is the same as multiplied by . Thus, the answer is .

The last two digits in the square of a number have a product of . Which of the following could NOT be the last digit of ?

If the last two digits of the squared number multiply to , then the digits must be factors of . The last digit of any square of a number ending in will be , which is not a factor of . Thus, the number cannot end in .

Solve: 3³

When using a cube root. 3³ becomes 3 * 3 * 3. 3 * 3 = 9 9 * 3 = 27

If (x - 3)2 = 64, what is a possible value of x?

When you square the following numbers, which one results in an irrational number?

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

The square of –2 is 4, of –3 is 9, and of 4 is 16. The sum of these squares is 29. The sum of (–2) + (–3) + (4) is –1. 29 – (–1) = 30

is between what two integers?

falls between and Therefore, is between and

Simplify the following:

is the same as multiplied by . Thus, the answer is .

The last two digits in the square of a number have a product of . Which of the following could NOT be the last digit of ?

If the last two digits of the squared number multiply to , then the digits must be factors of . The last digit of any square of a number ending in will be , which is not a factor of . Thus, the number cannot end in .

Solve: 3³

When using a cube root. 3³ becomes 3 * 3 * 3. 3 * 3 = 9 9 * 3 = 27

If (x - 3)2 = 64, what is a possible value of x?

When you square the following numbers, which one results in an irrational number?

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

How much larger is the sum of the squares of –2, –3, and 4 than the sum of these integers?

The square of –2 is 4, of –3 is 9, and of 4 is 16. The sum of these squares is 29. The sum of (–2) + (–3) + (4) is –1. 29 – (–1) = 30

is between what two integers?

falls between and Therefore, is between and

Simplify the following:

is the same as multiplied by . Thus, the answer is .

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

$\dpi{100} \small \sqrt{15}$ is between what two integers?

$\dpi{100} \small 3\times 3=9$

$\dpi{100} \small 4\times 4=16$

falls between and

Therefore, $\dpi{100} \small \sqrt{15}$ is between and

Simplify the following: $8^{2}$

$8^{2}$ is the same as multiplied by . Thus, the answer is .

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

$\dpi{100} \small \sqrt{15}$ is between what two integers?

$\dpi{100} \small 3\times 3=9$

$\dpi{100} \small 4\times 4=16$

falls between and

Therefore, $\dpi{100} \small \sqrt{15}$ is between and

Simplify the following: $8^{2}$

$8^{2}$ is the same as multiplied by . Thus, the answer is .

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

The square of –2 is 4, of –3 is 9, and of 4 is 16.

The sum of these squares is 29.

The sum of (–2) + (–3) + (4) is –1.

29 – (–1) = 30

$\dpi{100} \small \sqrt{15}$ is between what two integers?

$\dpi{100} \small 3\times 3=9$

$\dpi{100} \small 4\times 4=16$

falls between and

Therefore, $\dpi{100} \small \sqrt{15}$ is between and

Simplify the following: $8^{2}$

$8^{2}$ is the same as multiplied by . Thus, the answer is .