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LenaWriter [7]
4 years ago
12

Simplify completely. show your work. thank you for your help!​

Mathematics
2 answers:
Anton [14]4 years ago
8 0

Answer:

6\sqrt{15}

Step-by-step explanation:

Using the rule of radicals

\sqrt{a} × \sqrt{b} ⇔ \sqrt{ab} , then

\sqrt{60}

= \sqrt{4(15)}

= \sqrt{4} × \sqrt{15} = 2\sqrt{15} thus

3\sqrt{60}

= 3 × 2\sqrt{15}

= 6\sqrt{15}

Ierofanga [76]4 years ago
5 0

Answer:6 or decimal 23.23790

Step-by-step explanation:

the prime factorization of 60: 2^2 * 3 * 5

=3\sqrt{2^{2} }

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First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\  \\ =\sqrt{(8--5)^2+(-3-4)^2} \\  \\ =\sqrt{(13)^2+(-7)^2} \\  \\ =\sqrt{169+49} \\  \\ =\sqrt{218} \\  \\ \approx14.7648... \end{gathered}

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