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Calculate sqrt(60x)*sqrt(12x)*sqrt(63x)*sqrt(42x). Express your answer in simplest radical form in terms of x. Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter sqrt(14) as "sqrt(14)" or "sqrt{14}".

 Jan 22, 2022
 #1
avatar+2444 
+2

\( \sqrt{60x} = \sqrt{4} * \sqrt{15x} = 2\sqrt{15x}\) 

\(\sqrt{12x} = \sqrt{4} * \sqrt{3x} = 2\sqrt{3x}\)

\(\sqrt{63x} = \sqrt{9} * \sqrt{7x} = 3\sqrt{7x}\)

\(\sqrt{42x} = \sqrt{42x}\)

 

Now, multiply all the radicals and you get \(252x^2 \sqrt 30\).

 

I think...

 Jan 22, 2022
 #2
avatar+117849 
+2

Let's see

 

\(\sqrt{60x}*\sqrt{12x}*\sqrt{63x}*\sqrt{42x}\\ =\sqrt{60}*\sqrt{12}*\sqrt{63}*\sqrt{42}*\sqrt{x^4}\\ =2\sqrt{3*5}*2\sqrt{3}*3\sqrt{7}*\sqrt{7*6}*x^2\\ =2*2*3 *\sqrt{3*5*3*7*7*6}*x^2\\ =12 *3*7*\sqrt{5*6}*x^2\\ =12 *3*7*\sqrt{5*6}*x^2\\ =252\sqrt{30}\;x^2\)

 

There you go BilderBoi,    we are in full agreement   cool

 Jan 22, 2022

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