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square root of 6X times square root of 18X squared

simplifying radical expressions

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Jason T. | Jason Tutors Math & PhysicsJason Tutors Math & Physics
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Do you mean (sqrt(6x))*(sqrt(18x2)? If so you can multiply thne two together under one sqrt.

So you get sqrt(6*18*x*x2). Any perfect squares under the square root can be factored out. x2 is a perfect square so the square root of that is x and that comes out.

This gives you x * sqrt(6*18*x).

Let's see if we can factor out some perfect squares from 6*18. Breaking them both down we have

(3*2)*(3*3*2) = 32 * 22 * 3. The 32 and 22 become 3 and 2 when you factor them out. The other 3 stays under the square root.

So now our solution is 3*2*x*sqrt(3*x) = 6x * sqrt(3x)