Algebra Examples

Simplify square root of 27x^3y+x square root of 48xy
27x3y+x48xy27x3y+x48xy
Step 1
Simplify each term.
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Step 1.1
Rewrite 27x3y27x3y as (3x)2(3xy)(3x)2(3xy).
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Step 1.1.1
Factor 99 out of 2727.
9(3)x3y+x48xy9(3)x3y+x48xy
Step 1.1.2
Rewrite 99 as 3232.
323x3y+x48xy323x3y+x48xy
Step 1.1.3
Factor out x2x2.
323(x2x)y+x48xy323(x2x)y+x48xy
Step 1.1.4
Move 33.
32x23xy+x48xy32x23xy+x48xy
Step 1.1.5
Rewrite 32x232x2 as (3x)2(3x)2.
(3x)23xy+x48xy(3x)23xy+x48xy
Step 1.1.6
Add parentheses.
(3x)23(xy)+x48xy(3x)23(xy)+x48xy
Step 1.1.7
Add parentheses.
(3x)2(3xy)+x48xy(3x)2(3xy)+x48xy
(3x)2(3xy)+x48xy(3x)2(3xy)+x48xy
Step 1.2
Pull terms out from under the radical.
3x3xy+x48xy3x3xy+x48xy
Step 1.3
Rewrite 48xy as (22)2(3xy).
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Step 1.3.1
Factor 16 out of 48.
3x3xy+x16(3)xy
Step 1.3.2
Rewrite 16 as 42.
3x3xy+x423xy
Step 1.3.3
Rewrite 4 as 22.
3x3xy+x(22)23xy
Step 1.3.4
Add parentheses.
3x3xy+x(22)23(xy)
Step 1.3.5
Add parentheses.
3x3xy+x(22)2(3xy)
3x3xy+x(22)2(3xy)
Step 1.4
Pull terms out from under the radical.
3x3xy+x(223xy)
Step 1.5
Rewrite using the commutative property of multiplication.
3x3xy+22x3xy
Step 1.6
Raise 2 to the power of 2.
3x3xy+4x3xy
3x3xy+4x3xy
Step 2
Add 3x3xy and 4x3xy.
7x3xy
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