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

Math
20x4u55x3u9
Rewrite 20x4u5 as (2x2u2)2⋅(5u).
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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
Add parentheses.
(2x2u2)2⋅(5u)5x3u9
(2x2u2)2⋅(5u)5x3u9
Pull terms out from under the radical.
2x2u25u5x3u9
Rewrite 5x3u9 as (xu4)2⋅(5xu).
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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
Add parentheses.
2x2u25u(xu4)2⋅5(xu)
Add parentheses.
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.
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Move x.
2(x⋅x2)u25u(u45xu)
Multiply x by x2.
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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)
Add 1 and 2.
2x3u25u(u45xu)
2x3u25u(u45xu)
Multiply u2 by u4 by adding the exponents.
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Move u4.
2×3(u4u2)5u5xu
Use the power rule aman=am+n to combine exponents.
2x3u4+25u5xu
Add 4 and 2.
2x3u65u5xu
2x3u65u5xu
Multiply 2x3u65u5xu.
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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
Add 1 and 1.
2x3u625xu2
2x3u625xu2
Rewrite 25xu2 as (5u)2x.
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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.
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Move u.
2×3(u⋅u6)(5x)
Multiply u by u6.
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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)
Add 1 and 6.
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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