Mathematics Middle School

Please help me
Simplify each square root expression. Describe the simplified form of the expression as rational or irrational. In your final answer, include all of your work.
√121
√48
Simplify each cube root expression. Describe the simplified form of the expression as rational or irrational. In your final answer, include all of your work.
3√81
3√-64

Answers

Answer 1

Answer:

Sure, I'd be happy to help you with these problems!

Simplifying square root expressions:

√121 = 11

The square root of 121 is a rational number because it can be expressed as a ratio of two integers (11/1).

√48 = √(16*3) = √16 * √3 = 4√3

The square root of 48 is an irrational number because it cannot be expressed as a ratio of two integers.

Simplifying cube root expressions:

3√81 = 3√(3^4) = 33 = 9

The cube root of 81 is a rational number because it can be expressed as a ratio of two integers (9/1).

3√(-64) = 3√(-444) = 34√(-4) = 12i√2

The cube root of -64 is an irrational number because it cannot be expressed as a ratio of two integers. However, it can be expressed as a product of a rational number (4) and an imaginary number (i√2), where i is the imaginary unit (i.e., i^2 = -1). Therefore, the simplified form of this expression is an imaginary number.

Answer 2

1. √121:

To simplify this expression, we need to find the square root of 121. The square root of 121 is 11, since 11 * 11 = 121. Therefore, the simplified form of √121 is 11.

Since 11 is a whole number, it is considered a rational number.

2. √48:

To simplify this expression, we need to find the square root of 48. We can simplify it by factoring 48 into its prime factors: 48 = 2 * 2 * 2 * 2 * 3.

Taking out pairs of identical prime factors, we get √48 = √(2 * 2 * 2 * 2 * 3) = 2 * 2 * √3 = 4√3.

The simplified form of √48 is 4√3.

Since 4√3 cannot be expressed as a fraction, it is considered an irrational number.

Now let's simplify each cube root expression and describe the simplified form as rational or irrational.

3. 3√81:

To simplify this expression, we need to find the cube root of 81. The cube root of 81 is 4, since 4 * 4 * 4 = 81. Therefore, the simplified form of 3√81 is 4.

Since 4 is a whole number, it is considered a rational number.

4. 3√-64:

To simplify this expression, we need to find the cube root of -64. The cube root of -64 is -4, since -4 * -4 * -4 = -64. Therefore, the simplified form of 3√-64 is -4.

Since -4 is a whole number, it is considered a rational number.

In summary:

- √121 simplifies to 11, which is a rational number.

- √48 simplifies to 4√3, which is an irrational number.

- 3√81 simplifies to 4, which is a rational number.

- 3√-64 simplifies to -4, which is a rational number.

Related Questions

Michelle practiced all week to improve her typing speed. She estimated she could type 27 words per minute. When she took her typing test, she actually typed 30 words per minute. What is the percent error for Michelle's estimate?

If necessary, round your answer to the nearest tenth of a percent.

Answers

Answer:

90%

Step-by-step explanation:

The answer would be:
90%

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Answer:x=29

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x+3+x-1+x+1=90

3x+3-1+1=90

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Step-by-step explanation:

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Answer:

410.6 cubic cm

Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer: The area of the shaded region is 50.24 square centimeter

Step-by-step explanation:

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Answers

Answer:A=2b square root 2

Step-by-step explanation: the base is b and the exponent is 2 the factor b repeats2 time so the base is b and exponent is 2

A=2b square root 2 because base b is the root and that repeats 2 times

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A. 12ft
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Answers

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Answers

Answer: X - 2/3

Step-by-step explanation:

x is the number

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The keyword less tells you to subtract. So let’s your the variable Y for example. Your going to subtract 2/3 from Y. So that would be Y- 2/3!

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A 216 square feet
B 336 square feet
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D 576 square feet

Answers

Answer: 576 square feet

Step-by-step explanation:

576 because you have to do 6x8 then you get 48 which you multiply by the height (12) and you get 576

1. What is the median number of TVs in Mrs. Jamison's class?
2. What is the median number of TVs in Mr. Zimmerman's class?

Answers

1. median of 2
2. median of 3

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Answers

Answer:

11 4/7

Step-by-step explanation:

The answer is : 54.69

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Answers

Answer:

D

Step-by-step explanation:

Answer:

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K=2.5 because 5 divided by 2 is 2.5. You can even check this by dividing 12.5 by 5 and still get 2.5

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Suppose you bought a car for $72,227 and the value of the car has decreased by 97%. What is the new value of the car? Round your answer to the nearest hundredth.

Answers

Answer:

2167

Step-by-step explanation:

2166.8 is a 97% decrease of 72227.

Here is the answer.

2166.8

Can anyone solve this?

Answers

Me eleven
Pretty YEAH RESLLY PRETTY
it’s eleven! how do i know this?

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Answers

Hope this helped you!

The two ordered pairs are (4,-2) and (-2,2)

which angles are supplementary to each other? select all that apply

Answers

A supplementary angle is angles that when added together equals 180 degrees

The answers would be:
Angle 4 and 4

They are the only two angles that add up to 180 degree
Angle 4and5 are supplementary to each other

what is this (6x+4)+26=90 ?

Answers

Answer:

x=10

Step-by-step explanation:

(6x+4)+26=90

6x+4+26=90

6x+30-30=90-30

6x÷6=60÷6

x=10

Answer:

the answer is X=10

(6x+4)+26=90

6x +30=90

6x= 90÷30

6x=60

X = 60÷6

X= 10

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Answers

Answer: the second one.

Step-by-step explanation:

it means any number greater than or equal to 11. so it would be a closed circle going towards any number greater than 11 :)

Answer: 2

Step-by-step explanation:

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Answers

Answer:

1. c. 276ft

2.56ft

Step-by-step explanation:

1. I took the length and multiplied that by the width to get the area

2.

Answer:

1. C

2. D

Step-by-step explanation:

For question 1 you would multiply 23 by 12 because the area of a rectangle is base * height. To get 276 which is C.

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50 POINTS NO FAKE ANSWERS!!!!!!!!!!

Answers

Shakes are 2,8,24 mice are 5,20,60

the equivalente are 2:5, 8:20 and 24:60

Directions: Follow the instructions for the following inequalities.


1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9


2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)


3. -2 less than or equal to -2 Subtract 6 from both sides, then 8, and then 2


4. -4 < 8 Divide both sides by -4, then by -2


5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?

Answers

Answer:

1. 504 < 1512

2. 12 > 0

3. -2 = -2

4. -1 < 2

Step-by-step explanation:

Given that both sides are being changed by the same amount and sign, the sign never changes. They always have the same value.

The answer is -2 because after you multiply you have to divide

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Answer:it can be a trapezium it is a quadrilateral

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Step-by-step explanation:

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Answers

When two angles are supplementary, it means that the two angles add up to 180°.
Thus when angle m is 34° and angle n is (2x)° when angle m and angle n are supplementary,

angle m + angle n = 180°
34° + (2x)° = 180°

*minus 34° on both sides of the eqn*

(2x)° = 180°-34°
(2x)° = 146°

To find x, divide both sides of the eqn by 2
x= 146°/2
x= 73°

I hope this helps! Feel free to clarify if you have any questions!

The value of x is:

↬ 73

Solution:

If two angles are supplementary, that means that the sum of their measures is 180°.

We're given 2 angles:

[tex]\sf{\angle m}[/tex][tex]\sf{\angle n}[/tex]

And since they're supplementary, the following holds true:

[tex]\sf{\angle m + \angle n = 180}[/tex]

Next, we know that [tex]\sf{\angle m=34}[/tex], so we plug that in

[tex]\sf{34+\angle n = 180}[/tex]

Then, ∠n = 2x:

[tex]\sf{34+2x=180}[/tex]

Which is the same as

[tex]\sf{2x+34=180}[/tex]

Subtract 34 from each side

[tex]\sf{2x=146}[/tex]

Divide each side by 2

[tex]\sf{x=73}[/tex]

Hence, x = 73

Identify the least value, first quartile, median, third quartile, and greatest value of the data.
5, 1, 4, 0, 9, 0, −8, 5, 2, 4, −1, 10, 7, −5

Answers

The median based on the number lines given will be 3.
How to calculate the median?
It should be noted that the median simply means the number in the middle when the numbers are arranged in ascending or descending order.
The median will be:
-8, -5 -1, 0, 0, 1, 2, 4, 4, 5, 5, 7, 9, 10. Here, the median will be:
= (2 + 4)/2
= 3
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