How do I simplify radicals?

Answer:

Step 1: Find the prime factorization of the number inside the radical. Start by dividing the number by the first prime number 2 and continue dividing by 2 until you get a decimal or remainder. Then divide by 3, 5, 7, etc. until the only numbers left are prime numbers. Click on the link to see some examples of Prime Factorization. Also factor any variables inside the radical.

Step 2: Determine the index of the radical. The index tells you how many of a kind you need to put together to be able to move that number or variable from inside the radical to outside the radical. For example, if the index is 2 (a square root), then you need two of a kind to move from inside the radical to outside the radical. If the index is 3 (a cube root), then you need three of a kind to move from inside the radical to outside the radical.

Step 3: Move each group of numbers or variables from inside the radical to outside the radical. If there are nor enough numbers or variables to make a group of two, three, or whatever is needed, then leave those numbers or variables inside the radical. Notice that each group of numbers or variables gets written once when they move outside the radical because they are now one group.

Step 4: Simplify the expressions both inside and outside the radical by multiplying. Multiply all numbers and variables inside the radical together. Multiply all numbers and variables outside the radical together.

Example:

Example 1 – Simplify: Example 1

Step 1: Find the prime factorization of the number inside the radical.  

252=2*2*3*3*7

Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind.  

√252= √2*2*3*3*7

Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical.  

2*3√7

Step 4: Simplify the expressions both inside and outside the radical by multiplying.  

6√7

Pls Mark Brainliest

Please help me;(
If the measure of Angle F G H is 64 degrees and the measure of Angle E G D is (4 x + 8) degrees, what is the value of x? Lines E H and D F intersect at point G. 14 18 64 116

PLZ HELP ASAP IT IS TIMED

Mrs. Hanks bought 12-pound ham to serve for the holidays. She plans to serve each person 2/3 of a pound. The equation 2/3x = 12 can be used to determine x, the number of servings, What is the total number of serving she can make?

How do you do this help

PLEASE ANYONE HELP ME OUT WITH THIS QUESTION
Please Anyone Help Me Out With Digit 7

456.9 - 87.34
Soon please!!

Help me wit my homework thx

Help!!

What is equivalent to the expression -2x(-4 + x)

A. 8x - 4x
B. -8x + 4x²
C. -8x + 2x²
D. 8x + 2x²
E. 8x - 2x²

Which calculation results in the best estimate of 148% of 203? (200) (140 percent) = (200) (100 percent + 40 percent) = (200) (100 percent) + (200) (40 percent) = (200) (1.0) + (200) (0.4) = 200 + 80 = 280 (210) (140 percent) = (210) (100 percent + 40 percent) = (210) (100 percent) + (210) (40 percent) = (210) (1.0) + (210) (0.4) = 210 + 84 = 294 (200) (150 percent) = (200) (100 percent + 50 percent) = (200) (100 percent) + (200) (50 percent) = (200) (1) + (200) (one-half) = 200 + 100 + 300 (210) (150 percent) = (210) (100 percent + 50 percent) = (210) (100 percent) + (210) (50 percent) = (210) (1) + (210) (one-half) = 210 + 105 = 315

22 points! Which expressions will help you find the surface area of this right triangular prism? Select all that apply.



11 × 3
× 3 × 5
4 × 11
5 × 11

A project will take a total of 720 person-days to complete. If the project must be completed in 30 days, how many people must be employed? PLEASE HURRY

Please help with question please. It’s due tomorrow at 8:30 AM so please help.

order the values from least to greatest |-16|, 10, |25|, -16, |-43|

Emmett deposited $90 in an account earning 4% interest compounded annually.

To the nearest cent, how much INTEREST will he earn after two years? (Hint: You are finding the interest, not the total amount in the account.)
Responses

$7.34


$97.34


$10.34


$90.00

X Y
-7 0
0 1

What is the slope of the linear function represented in
the table?
*-7
07/1
01/1
07

Which scenario can be modeled by the linear function
y = -15x + 500?

A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.

B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.

C. A carpet cleaning service charges $500 plus an additional $15 for every hour.

D. A membership fee for a movie streaming service is free, but each rental costs $15.

Kyle has three pieces of rope. The lengths of the ropes are 241.6 centimeters, 241.38 centimeters, and 264.7 centimeters.

What is the difference in length between the longest and shortest pieces of rope?

Can Someone Help Me Please? I am offering 100 points!
Geraldine is graphing the inequality x less-than 6. Which statements below describe steps she may take to graph the inequality correctly? Check all that apply.
Draw an open circle at 6.
Draw a closed circle at 6.
Shade all numbers less than 6.
Shade all numbers greater than 6.
Shade all numbers to the right of 6.
Shade all numbers to the left of 6.

Use the word MISSISSIPPI to match each ratio.
(picture below)

PLS HELP 50 POINTS!!! also PLEASE provide an explanation or work with your answer!!! **i hate algebra >:(**

Tammy graphs the function h(x) = x² + 9. Sarah graphs the function g(x) = (x + 9)². Which statements are true regarding the two graphs? Select three options.


Tammy’s graph is a vertical translation of f(x) = x².

Sarah’s graph is a vertical translation of f(x) = x².

Tammy's graph moved 9 units from f(x) = x² in a positive direction.

Sarah's graph moved 9 units from f(x) = x² in a positive direction.

Tammy’s graph has a y-intercept of 9.

Sarah's graph has a y-intercept of 9.

Giving 50 points for who ever answer's this ill give brainiest. PICTURE INCLUDED

pls help me with number 3

i know it shows i already answered it but i just accidentally clicked it.

Magdeline wants to know if the number of words on a page in her art book is generally more than the number of words on a page in her science book. She takes a random sample of 25 pages in each book and then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.

Book Mean Median Mean Absolute Deviation
Art 68.7 50 15.4
Science 54.2 55 7.9


She claims that because the mean number of words on each page in the art book is greater than the mean number of words on each page in the science book, the art book has more words per page. Based on the data, is this a valid inference? (10 points)

Yes, because the mean is larger in the art book
No, because the mean is larger in the art book
Yes, because there is a lot of variability in the art book data
No, because there is a lot of variability in the art book data

Select the correct answer.
Molly rewrote the equation as shown:
-50 + 11 =8-30
50 +11+30=8-30-30
Which property did she use to rewrite the equation?

Solve for x.
-30=5(x+1)

Evaluate (4a2 + b) ÷ c , when a= −2, b= −1, and c= 5.

Help pls!!!! I’m super stuck

Mary's Time Spent Exercising
Week 1
Sun
Week 2
0 min
Mon
0 min
45 min
Tue
45 min
45 min
Wed
40 min
Thu
45 min
50 min
50 min
Which of the following best explains why the mean is NOT an appropriate indicator of how much time Mary spends exercising on a typical day?
Fri
40 min
35 min
Sat
50 min
0 min
35 min

ANSWER PLEASE BEFORE 2/14!!!!

Tamara likes to go hiking and tries to hike for at least 30 minutes every week. On Tuesday, she hiked for 1 mile in the morning and 3 miles in the evening. On Thursday, she hiked with a friend for 4 miles. On Saturday she hiked for 5 miles. On Sunday, she hiked for 4 miles. She also hiked for an extra 10 minutes on Sunday night. If she hiked for a total of 350 minutes all week and it takes her the same amount of time to hike each mile, how many minutes does it take her to hike each mile?

Robin wants to buy a membership at a carwash this summer so that she can keep her car clean. She compared deals from Speedy Clean Carwash and Sudsy Bubbles Carwash to decide which membership to get. Robin arranged the information in the tables below.
How many times will Robin need to wash her car to spend the same amount at both carwashes?
P.S.: I attached the table below:)