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# find the square root of 8!/70 (reminder:the number n! is the product of integers from 1 to n for example, 5! = 5*4*3*2*1=120

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find the square root of 8!/70 (reminder:the number n! is the product of integers from 1 to n for example, 5! = 5*4*3*2*1=120

Apr 17, 2022

#1
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8! / 70 ==40,320 / 70 ==576

Sqrt(576) ==24

Apr 17, 2022
#2
+9459
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$$\begin{array}{cl} &\sqrt{\dfrac{8!}{70}}\\ =& \sqrt{\dfrac{2\times 3\times 4\times 5\times 6\times 7\times 8}{2\times 5\times 7}}\\ =& \sqrt{3\times 4\times 6\times 8}\\ =& \sqrt{3\times 4 \times (2\times 3)\times (2\times 4)}\\ =& \sqrt{(2\times 2) \times ((3\times 4)\times (3\times 4))}\\ =& \sqrt{2^2 \times 12^2}\\ =& \sqrt{24^2}\\ =& 24 \end{array}$$

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Apr 17, 2022