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Temka [501]
3 years ago
9

What pattern do you notice in the numbers below? 1 = 1 × 1, and 1 × 1 × 1, and 1 × 1 × 1 64 = 8 × 8, and 4 × 4 × 4 729 = 27 × 27

, and 9 × 9 × 9 4,096 = 64 × 64, and 16 × 16 × 16 A. They are perfect squares. B. They are perfect cubes. C. They are both perfect squares and perfect cubes. D. They are neither perfect squares nor perfect cubes.
Mathematics
1 answer:
11111nata11111 [884]3 years ago
4 0

Answer:

<h3>C. They are both perfect squares and perfect cubes.</h3>

Step-by-step explanation:

Perfect squares are numbers that their square root can be found easily without any remainder.

Given the following patterns;

1*1 = 1  and 1*1*1 = 1

It can be seen that 1 is 1 perfect square since 1*1 = 1² = 1

Also 1 is perfect cube since 1*1*1 = 1³ = 1 (cube of the value gives 1)

Similarly for the expression;

8*8 = 64

8² = 64 (since the square of 8 gives 64, then 64 is known to be a perfect square)

Also 4*4*4 = 64

i.e 4³ = 64 (This shows that the cube root of 64 is 4 making it a perfect cube since we can get a whole number for the cube root of 64)

The same is applicable for other expressions 729 = 27 × 27, and 9 × 9 × 9, 4,096 = 64 × 64, and 16 × 16 × 16

This values are easily expressed as a constant multiple of a number showing that they are both perfect squares and perfect cubes.

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8 0
3 years ago
Solve for x in the equation x squared + 2 x + 1 = 17.
Papessa [141]

Answer:

x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\

Step-by-step explanation:

given equation

x^2 +2x +1 = 17

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the solution for quadratic equation

ax^2 + bx + c = 0 is given by

x = x = -b + \sqrt{b^2 - 4ac} /2a \\\\and \ \\-b - \sqrt{b^2 - 4ac} /2a

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in our problem

a = 1

b = 2

c = -16

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thus value of x is

x = - 1 + \sqrt{17}\\and\\x = - 1 - \sqrt{17}\\

3 0
3 years ago
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