Question

Which are perfect cubes? Check all that apply. 64 x16 8x3 27x4 81x6 125x9

Answer 1

Answer:

A,C,F

Step-by-step explanation: I took the test :)

Answer 2

The expression 64 is perfect cube of 3.

The expression $8x^{3]$ is the perfect cube of $(2x)^{3}$.

The expression $12x^{9}$ is perfect square of $(5x^{3})^{3}$

We have to determine, which to the following is perfect cube.

According to the question,

A perfect cube is an integer that is equal to some other integer raised to the third power.

To obtain the perfect cubes of the expression, it can be determined in following steps.

The given expression is 64.

To convert it into perfect square written in small factor parts.

Therefore, 64 written as,

$= 64\\\\= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\\\= (2)^{3} \times (2)^{3}\\\\= (2\times 2)^{3}\\\\=( 4)^{3}$

The expression 64 is perfect cube of 3.

The given expression is 16x.

To convert it into perfect square written in small factor parts.

Then,

16x can be written as,

$= 16x \\\\= 2\times 2\times 2\times 2\times x\\\\= 2x.(2)^{3}$

The expression 16x is not perfect cube.

The given expression is $8x^{3]$.

To convert it into perfect square written in small factor parts.

Then,

$8x^{3}$ can be written as,

$= 8x^{3}\\\\= 2 \times 2 \times 2 \times x^{3}\\\\= (2)^3 \times {x^{3}}\\\\= (2x)^{3}$

The expression $8x^{3]$ is the perfect cube of $(2x)^{3}$.

The given expression is $27x^{4}$

To convert it into perfect square written in small factor parts.

Then,

$27x^{4}$ can be written as,

$= 27x^{4}\\\\= 3 \times3 \times3 \times x^{4}\\\\= (3)^{3} \times x \times x^{3}\\\\= x \times (3x)^3$

The expression $27x^{4}$ is not a perfect cube.

The given expression is $81x^{6}$

To convert it into perfect square written in small factor parts.

Then,

$81x^6$ can be written as,

$= 81x^{6}\\\\= 3 \times3 \times3 \times3 \times x^{6}\\\\= 3.(3)^{3} \times x^{3} \times x^{3}\\\\= 3 \times ( 3x^{2}) ^{3}$

The expression $81x^{6}$ is not a perfect cube.

The given expression is $81x^{6}$

To convert it into perfect square written in small factor parts.

Then,

$125x^{9}$ can be written as,

$=125x^{9}\\\\= 5 \times 5 \times 5 \times x^{3} \times x^{3} \times x^{3}\\\\= (5x^{3})^{3}$

The expression $12x^{9}$ is perfect square of $(5x^{3})^{3}$

To know more about perfect square click the link given below.

https://brainly.com/question/16780291