Find the difference:

Question

16 square root of 23 end root minus 1 square root of 23 end root. Explain your reason, no slashes!!! EVER!!!

Answer 1

To find the difference \( 16 \sqrt{23} - 1 \sqrt{23} \), we can combine the terms since they are like terms.

1. Identify the coefficients of \( \sqrt{23} \):

   • The first term has a coefficient of 16, and the second term has a coefficient of 1.

2. Subtract the coefficients:

   • \( 16 - 1 = 15 \)

3. Combine the results:

   • So, \( 16 \sqrt{23} - 1 \sqrt{23} = 15 \sqrt{23} \)

Therefore, the difference is \( 15 \sqrt{23} \).

Answer 2

NO SLASHES!!!!

Answer 3

I apologize for that. Let’s rewrite it without slashes.

To find the difference of sixteen square root of twenty-three minus one square root of twenty-three, we combine the terms since they are like terms.

First, we identify the coefficients of square root of twenty-three:

• The first term has a coefficient of sixteen, and the second term has a coefficient of one.

Next, we subtract the coefficients:

• Sixteen minus one equals fifteen.

Finally, we combine the results:

• So, sixteen square root of twenty-three minus one square root of twenty-three equals fifteen square root of twenty-three.

Therefore, the difference is fifteen square root of twenty-three.

Answer 4

Find the difference.

15 cube root of 3 end root minus 7 cube root of 3 end root

Answer 5

To find the difference of fifteen cube root of three minus seven cube root of three, we can combine the terms since they are like terms.

First, we identify the coefficients of cube root of three:

• The first term has a coefficient of fifteen, and the second term has a coefficient of seven.

Next, we subtract the coefficients:

• Fifteen minus seven equals eight.

Finally, we combine the results:

• So, fifteen cube root of three minus seven cube root of three equals eight cube root of three.

Therefore, the difference is eight cube root of three.

Answer 6

and why is that?

Answer 7

The reason we can combine the terms \( 15 \) cube root of \( 3 \) and \( 7 \) cube root of \( 3 \) is that they are like terms. Like terms are terms that have the same variable or radical part. In this case, both terms involve the cube root of \( 3 \).

1. Like Terms: Since both terms contain the same radical, cube root of \( 3 \), we can treat the coefficients (the numbers in front) as regular numbers when performing arithmetic operations.

2. Subtracting Coefficients: When we subtract the coefficients, we simply perform the subtraction as we would with ordinary numbers. In this case:

   • The coefficient from the first term is \( 15 \).
   • The coefficient from the second term is \( 7 \).
   • So, \( 15 - 7 = 8 \).

3. Combining the Terms: After finding the difference in coefficients, we then attach that result to the common radical part:

   • The result is \( 8 \) cube root of \( 3 \).

This works because the radical part does not change when you are combining like terms; only the coefficients are affected by the arithmetic operation.

Thus, the final result, eight cube root of three, accurately represents the combined value of the two original terms.

Answer 8

NO SLASHES UNDER ANY CIRCUMSTANCES!!!

Answer 9

Understood! I apologize for that oversight.

To explain why fifteen cube root of three minus seven cube root of three equals eight cube root of three:

1. Like Terms: Both terms have the same radical part, which is cube root of three. This allows us to combine them.

2. Subtracting Coefficients: We subtract the coefficients directly. The first term has a coefficient of fifteen, and the second term has a coefficient of seven. When we subtract these coefficients:

   • Fifteen minus seven equals eight.

3. Combining the Results: After subtracting the coefficients, we attach the common radical part, which is cube root of three. So, we have eight cube root of three.

Therefore, the result is eight cube root of three because we can combine like terms by subtracting their coefficients. Thank you for your patience!