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2 years ago

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

Mathematics

2 answers:

vovangra [49]2 years ago

6 0

Answer:

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.

PilotLPTM [1.2K]2 years ago

5 0

Answer:

The correct answer is 60 -21√6

Step-by-step explanation:

It is given that,

3√2(5√8 - 7√3)

<u>To find the product</u>

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

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To calculate the angles of the given triangle, we can use the law of cosines:

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$\begin{gathered} \cos (B)=\frac{8^2+2^2-9^2}{2\cdot8\cdot2} \\ \cos (B)=\frac{13}{32} \\ B=\cos ^{-1}(\frac{13}{32}) \\ B=113.9\degree \\ \text{Rounding:} \\ B=114\degree \end{gathered}$ $\begin{gathered} \cos (C)=\frac{2^2+9^2-8^2}{2\cdot2\cdot9} \\ \cos (C)=\frac{21}{36} \\ C=\cos ^{-1}(\frac{21}{36}) \\ C=54.3 \\ \text{Rounding:} \\ C=\text{ 54}\degree \end{gathered}$

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