Here are the steps required for Simplifying Radicals:
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. 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.
Shorter version:
Step 1: Find the prime factorization of the number inside the radical.
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.
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.
Step 4: Simplify the expressions both inside and outside the radical by multiplying.
Answer:
Associative Property of Multiplication
Step-by-step explanation:
We are given three numbers-a,b,c.
We are given the property (ab)c = a(bc)
This implies that on the left hand side we first multiply a and b and then multiply the result by c. On the right side of the equation, we first multiply b and c and multiply a with the product of b and c.
As per the given property, the result in both the cases is the same.
This signifies the associative property of multiplication where the result is independent of the order of operation.
Let
x------> amount of <span> big marbles in the box
y------> </span>amount of small marbles in the box
R----> amount of small marbles that are red in the box
B----> amount of small marbles that are blue in the box
we know that
x=45+(3/4)*x----> x-(3/4)*x=45----> x/4=45-----> x=180
R+B=y-----> equation 1
R=(2/5)*y---> equation 2
B=(3/5)*y---> equation 3
B=R+24----> equation 4
substitute equation 2 in equation 1
[(2/5)*y]+B=y----> equation 5
substitute equation 2 in equation 4
B=[(2/5)*y]+24----> equation 6
resolve the system
[(2/5)*y]+B=y---> multiply by 5----> 2y+5B=5y----> 3y=5B
B=[(2/5)*y]+24----> multiply by 5----> 5B=2y+120
using a graph tool
see the attached figure
the solution is
B=72
y=120
R=y-B----> R=48
total marbies=x+y-----> 180+120-----> 300
tota; big marbies=180
<span>percent of the marbles are big marbles
</span>if 100%-----------> 300
X----------------> 180
x=180*100/300-----> x=60%
the answer is60%
0.8 is greater than 0.08. Hope this is helpful!