# Simplify square root of ((3000*4)/300)/p

3000⋅4300p
Reduce the expression by cancelling the common factors.
Reduce the expression 3000⋅4300 by cancelling the common factors.
Factor 300 out of 3000⋅4.
300(10⋅4)300p
Factor 300 out of 300.
300(10⋅4)300(1)p
Cancel the common factor.
300(10⋅4)300⋅1p
Rewrite the expression.
10⋅41p
10⋅41p
Divide 10⋅4 by 1.
10⋅4p
10⋅4p
Multiply 10 by 4.
40p
Rewrite 40p as 40p.
40p
Simplify the numerator.
Rewrite 40 as 22⋅10.
Factor 4 out of 40.
4(10)p
Rewrite 4 as 22.
22⋅10p
22⋅10p
Pull terms out from under the radical.
210p
210p
Multiply 210p by pp.
210p⋅pp
Combine and simplify the denominator.
Multiply 210p and pp.
210ppp
Raise p to the power of 1.
210pp1p
Raise p to the power of 1.
210pp1p1
Use the power rule aman=am+n to combine exponents.
210pp1+1
210pp2
Rewrite p2 as p.
Use axn=axn to rewrite p as p12.
210p(p12)2
Apply the power rule and multiply exponents, (am)n=amn.
210pp12⋅2
Combine 12 and 2.
210pp22
Cancel the common factor of 2.
Cancel the common factor.
210pp22
Divide 1 by 1.
210pp1
210pp1
Simplify.
210pp
210pp
210pp
Combine using the product rule for radicals.
2p⋅10p
Move 10 to the left of p.
210pp
Simplify square root of ((3000*4)/300)/p

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