Simplifying Nonperfect Roots
1 answer:
Short Answer:Choice C [Third one down]
Remark
Start with the number so I can talk about the basic principle at work. The way to work it is to factor 162 into prime factors and hope there are at least 3 that are the same.
162 = 2 * 81
162 = 2 * 3 * 3 * 3 * 3
Now When you take the cube root of that, you get![\sqrt[3]{2*2*2*2*3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B2%2A2%2A2%2A2%2A3%7D%20)
Here's the rule for a cube root. For every 3 prime factors under the cuberoot sign, you take out one and throw the other two away. So for cube root of 81,
you would factor it as ∛(81) = ∛(3 * 3 * 3 * 3) = 3∛3.
So out of four 3s under the cube root sign, you have 1 outside the root sign and one inside the root sign. 2 of the four 3s have been thrown away.
Continuation.
X first
You want 2 xs outside the root sign
∛(x * x * x * x * x *x ) = (x * x) You have thrown away 2 xs for every x outside the cube root sign
C = 6 There are no left overs.
Y second
For the ys, you need 1 outside and 2 inside the root sign. that's because you need 5 altogether.
∛(y * y * y * y * y) = y ∛y^2
Answer
c = 6; d = 2
Choice C <<<<<< answer
Remark
Start with the number so I can talk about the basic principle at work. The way to work it is to factor 162 into prime factors and hope there are at least 3 that are the same.
162 = 2 * 81
162 = 2 * 3 * 3 * 3 * 3
Now When you take the cube root of that, you get
Here's the rule for a cube root. For every 3 prime factors under the cuberoot sign, you take out one and throw the other two away. So for cube root of 81,
you would factor it as ∛(81) = ∛(3 * 3 * 3 * 3) = 3∛3.
So out of four 3s under the cube root sign, you have 1 outside the root sign and one inside the root sign. 2 of the four 3s have been thrown away.
Continuation.
X first
You want 2 xs outside the root sign
∛(x * x * x * x * x *x ) = (x * x) You have thrown away 2 xs for every x outside the cube root sign
C = 6 There are no left overs.
Y second
For the ys, you need 1 outside and 2 inside the root sign. that's because you need 5 altogether.
∛(y * y * y * y * y) = y ∛y^2
Answer
c = 6; d = 2
Choice C <<<<<< answer
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Answer:
The correct option are;
On a coordinate plane, a cubic function has an x-intercept of (0, 0)
On a coordinate plane, an oval is in quadrant 1
Step-by-step explanation:
Rotational symmetry of a shape is a shape that when it is rotated on its axis to a given angle less than one complete revolution, the shape looks exactly like the pre-image or original appearance of the shape
For a cubic function that has x-intercept = (0, 0) we have;
y = f(x) = a·x³ + b·x² + c·x
Has the shape f a fan blade and therefore, looks the sane when rotated when rotated through 180°
The shape of an oval looks the same when rotated through 180°
