anonymous
  • anonymous
how would u simplify this radical form? sqrt{45x^2}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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campbell_st
  • campbell_st
\[\sqrt{45x^2} = \sqrt{9 \times 5 \times x^2 } = \sqrt{9} \times \sqrt{x^2} \times \sqrt{5}\] you can find the square root of 9 and x^2 so the answer is \[3x \sqrt{?}\]
anonymous
  • anonymous
good ths wt i did
ChrisS
  • ChrisS
So you would want to start by breaking this up as much as possible... I'd start by separating the coefficient from the variable \[\sqrt{45x^{2}}=\sqrt{45}\sqrt{x^{2}}\] Now 45 isn't a perfect square, but it can be factored and one of it's factors is a perfect square. Also the square root of x^2 is x. \[x*\sqrt{45}=x*\sqrt{9}\sqrt{5}\] and 9 is a perfect square so you can simplify that further and you will get \[3x \sqrt{5}\]

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anonymous
  • anonymous
That is usually the way it is done, but technically, \[\sqrt{x^2}=|x|\]which may make the desired answer \[3\sqrt{5}|x|\]
ChrisS
  • ChrisS
In general \[\sqrt{x}\] is accepted to mean the positive square root of x.
anonymous
  • anonymous
That's exactly the convention, and that's also the reason that the square root of x^2 is the absolute value of x. If x is negative, the square root of its square is its opposite.
ChrisS
  • ChrisS
I gotcha. Which is why then the answer as you described it would be the absolute value of x as opposed to + or - x.

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