# Simplify square root of 20x^4u^5 square root of 5x^3u^9

20x4u55x3u9
Rewrite 20x4u5 as (2x2u2)2⋅(5u).
Factor 4 out of 20.
4(5)x4u55x3u9
Rewrite 4 as 22.
22⋅5x4u55x3u9
Rewrite x4 as (x2)2.
22⋅5(x2)2u55x3u9
Factor out u4.
22⋅5(x2)2(u4u)5x3u9
Rewrite u4 as (u2)2.
22⋅5(x2)2((u2)2u)5x3u9
Move 5.
22(x2)2(u2)2⋅5u5x3u9
Rewrite 22(x2)2(u2)2 as (2x2u2)2.
(2x2u2)2⋅5u5x3u9
(2x2u2)2⋅(5u)5x3u9
(2x2u2)2⋅(5u)5x3u9
Pull terms out from under the radical.
2x2u25u5x3u9
Rewrite 5x3u9 as (xu4)2⋅(5xu).
Factor out x2.
2x2u25u5(x2x)u9
Factor out u8.
2x2u25u5(x2x)(u8u)
Rewrite u8 as (u4)2.
2x2u25u5(x2x)((u4)2u)
Move x.
2x2u25u5(x2)(u4)2xu
Move 5.
2x2u25ux2(u4)2⋅5xu
Rewrite (x2)(u4)2 as (xu4)2.
2x2u25u(xu4)2⋅5xu
2x2u25u(xu4)2⋅5(xu)
2x2u25u(xu4)2⋅(5xu)
2x2u25u(xu4)2⋅(5xu)
Pull terms out from under the radical.
2x2u25u(xu45xu)
Multiply x2 by x by adding the exponents.
Move x.
2(x⋅x2)u25u(u45xu)
Multiply x by x2.
Raise x to the power of 1.
2(x1x2)u25u(u45xu)
Use the power rule aman=am+n to combine exponents.
2×1+2u25u(u45xu)
2×1+2u25u(u45xu)
2x3u25u(u45xu)
2x3u25u(u45xu)
Multiply u2 by u4 by adding the exponents.
Move u4.
2×3(u4u2)5u5xu
Use the power rule aman=am+n to combine exponents.
2x3u4+25u5xu
2x3u65u5xu
2x3u65u5xu
Multiply 2x3u65u5xu.
Combine using the product rule for radicals.
2x3u65xu(5u)
Multiply 5 by 5.
2x3u625xu⋅u
Raise u to the power of 1.
2x3u625x(u1u)
Raise u to the power of 1.
2x3u625x(u1u1)
Use the power rule aman=am+n to combine exponents.
2x3u625xu1+1
2x3u625xu2
2x3u625xu2
Rewrite 25xu2 as (5u)2x.
Rewrite 25 as 52.
2x3u652xu2
Move x.
2x3u652u2x
Rewrite 52u2 as (5u)2.
2x3u6(5u)2x
2x3u6(5u)2x
Pull terms out from under the radical.
2x3u6(5ux)
Multiply u6 by u by adding the exponents.
Move u.
2×3(u⋅u6)(5x)
Multiply u by u6.
Raise u to the power of 1.
2×3(u1u6)(5x)
Use the power rule aman=am+n to combine exponents.
2x3u1+6(5x)
2x3u1+6(5x)
2x3u7(5x)
2x3u7(5x)
Multiply 5 by 2.
10x3u7x
Simplify square root of 20x^4u^5 square root of 5x^3u^9

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