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How do you know a radical expression is in simplest form?

Answer: To know whether a radical expression is in simplest form or not you should put the numbers and letters inside the radical in terms of prime factors. Then, the radical expression is in the simplest form if all the numbers and letters inside the radical are prime factors with a power less than the index of the radical

Explanation:

Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified

For example simplify the following radical in its simplest form:

$\sqrt[5]{3645 a^8b^7c^3}$

1) Factor 3645 in its prime factors: 3645 = 3^6 * 5

2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:

- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical

3) since the factor 5 has power 1 it can not leave the radical

4) the power of a is 8, then:

8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.

5) the power of b is 7, then:

7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical

6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.

7) the expression simplified to its simplest form is

$3ab \sqrt[5]{3.5.a^3b^2c^3}$

And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.

7 0

2 years ago

Read 2 more answers

A company is to hire two employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of t

Softa [21]

Answer:

i) Probability that both candidates employed are women = 5/14

ii) Probability that the second candidate is a woman = 5/8

iii) Probability that the first candidate is a woman given that second one is a woman = 4/5

Step-by-step explanation:

Let the probability that a man is employed be P(M) = 3/8

Probability that a woman is employed P(W) = 5/8

a) Probability that both candidates employed are women = (5/8) × (4/7) = 5/14

b) Probability that the second candidate is a woman = (probability that first candidate is a man and second candidate is a woman) + (probability that first candidate is a woman & second candidate is a woman)

= (3/8)(5/7) + (5/8)(4/7) = (15/56) + (20/56) = 35/56 = 5/8

c) Probability that the first candidate is a woman given that second one is a woman

Given that the second candidate was a women, means that the first candidate-women was selected among other four women.

Probability = (4/8)/(5/8) = 4/5

7 0

2 years ago

Plot the image of D under a dilation about the origin (0,0) with a scale factor of 2

ElenaW [278]

(-6,-4)

If you dilate a point, (c,d) about (a,b) by a scale factor by k. You'll going to subtract each coordinates where the point will be dilated about (a,b) from the point (c,d) and then multiply them by k. This would be the formula if you want: (k(c -a), k(b -d))

Let's say F is the dilation of D about the origin or (0,0) then the x coordinate of F would be

$x = 2( - 3 - 0) \\ x = 2( - 3) \\ x = - 6$

This would be the y coordinate of F:

$y = 2( - 2 - 0) \\ y = 2( - 2) \\ y = - 4$

Thus the coordinates of F is (-6,-4)

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2 years ago

The question is...................

Norma-Jean [14]

B is dilated by a factor of 5

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2 years ago

In the diagram, polygon ABCD is flipped over a line of reflection to make a polygon with vertices at A′, B′, C′, and D′. Points

DIA [1.3K]

<span>if point A( 2,2) is reflected across the line Y then the new position A' is (-2,2) and the distance AY = distance A'Y if A is reflected across line R it is now at point B and the distance AR = distance BR lets say the point A(2,2) was perpendicular to the line R at the point (1, 4) then when reflected the point A now at location B will have coordinates</span><span>when flipped over a line of reflection the lengths are still the same the point to the line of reflection is the same length as the line of reflection to the reflected position the distance from the original point to the reflected point is twice the distance from the original point to the line of reflection cannot see your polygon. here is an example

</span>

7 0

2 years ago