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2 years ago

Simplify 5 √16 + 12 √54 - 3 √8

Mathematics

1 answer:

USPshnik [31]2 years ago

8 0

20+36. l6-6/2

v. v

decimal form

99.69634936

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Which are sums of perfect cubes? Check all that apply. 8x6 27 x9 1 81x3 16x6 x6 x3 27x9 x12 9x3 27x9.

Black_prince [1.1K]

The equations which are sums of perfect cubes are as follows;

$\rm 8x^6+27x^9+1$

$\rm x^6+x^3$

$\rm 27x^9+x^{12}$

<h3>Perfect cubes;</h3>

Perfect cubes are the numbers that are the triple product of the same number.

We have to determine

Which are sums of perfect cubes?

1. The given equation is $\rm 8x^6+27x^9+1$ .

The equation can be written as;

$\rm 8x^6+27x^9+1\\\\2^3(x^2)^3+3^3(x^3)^3+1^3$

All the terms in the expression are can be represented as perfect cubes.

2. The given equation is $\rm 81x^3+16x^6$ .

The equation can be written as;

$\rm 81x^3+16x^6\\\\9^2x^3+4^2(x^2)3$

In this, all the terms are not perfect cubes, some of them are squares.

3. The given equation is $\rm x^6+x^3$ .

The equation can be written as;

$\rm x^6+x^3\\\\(x^2)^3+x^3$

All the terms in the expression are perfect cubes.

4. The given equation is $\rm 27x^9+x^{12}$ .

The equation can be written as;

$\rm 27x^9+x^{12}\\\\3^3(x^3)^3+(x^4)^3$

All the terms in the expression are perfect cubes.

5. The given equation is $\rm 9x^3+27x^9$ .

The equation can be written as;

$\rm 9x^3+27x^9\\\\3^2x^3+3^3(x^3)^3$

In this, all the terms are not perfect cubes, some of them are squares too.

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

brainly.com/question/4701925

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