What is the following product? 3√2 (5√8-7√3)

The correct answer is 60 - 21√6

Step-by-step explanation:

It is given that,

3√2 (5√8 - 7√3)

To find the product

We have

3√2 (5√8 - 7√3) = 3√2 (5√8) - 3√2 (7√3)

= 3*5√ (2 * 8) - 3 * 7 √2 * 3

= 15√16 - 21√6

= 15 * 4 - 21√6

= 60 - 21√6

Therefore 3√2 (5√8 - 7√3) = 60 - 21√6

The correct answer is 60 - 21√6

3√2 (5√8-7√3) = 60 - 21√6

Step-by-step explanation:

We need to find the product of 3√2 (5√8-7√3). The distributive property states that: A (B+C) = AB + AC.

Then, by using the distributive propertive we have that:

3√2 (5√8-7√3) = 3√2 * 5√8 - 3√2 * 7√3 = 15√8√2 - 21√2√3.

Also, we know that: √A√B = √AB. Using this:

15√8√2 - 21√2√3 = 15√16 - 21√6 = 60 - 21√6.