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Marina CMI [18]
3 years ago
12

Show all steps question is in the photo.

Mathematics
2 answers:
Lady bird [3.3K]3 years ago
5 0

\\ \sf\longmapsto \sqrt{108x^2y^3}-\sqrt{12x^2y^3}+x\sqrt{75y^3}

\\ \sf\longmapsto \sqrt{2\times 2\times 3\times 3\times 3\times x\times x\times y\times y\times y}-\sqrt{2\times 2\times 3\times x\times x\times y\times y\times y}+\sqrt{5\times 5\times 3\times y\times y\times y}

\\ \sf\longmapsto 6\sqrt{3}xy\sqrt{y}-2\sqrt{3}xy\sqrt{y}+5\sqrt{3}xy\sqrt{y}

\\ \sf\longmapsto \sqrt{3}xy\sqrt{y}(6-2+5)

\\ \sf\longmapsto 9\sqrt{3}xy\sqrt{y}

belka [17]3 years ago
3 0

Answer:

{ \rm{ \sqrt{108 {x}^{2}  {y}^{3} } -  \sqrt{12 {x}^{2} {y}^{3}  }  + x \sqrt{75 {y}^{3} }  }} \\  \\  = { \rm{\sqrt{(36 \times 3) {x}^{2}  {y}^{3} } -  \sqrt{(4 \times 3) {x}^{2} {y}^{3}  }  + x \sqrt{(3 \times 25)}   {y}^{3} }} \\  \\  = { \rm{ \sqrt{ {x}^{2}  {y}^{3} } ( \sqrt{36 \times 3}  -  \sqrt{4 \times 3}  +  \sqrt{3 \times 25} }}) \\  \\ { =  \rm{x {y}^{ \frac{3}{2} } (6 \sqrt{3} - 2 \sqrt{3}  + 5 \sqrt{3} ) }} \\  \\  = { \rm{x {y}^{ \frac{3}{2} }  \{(6 - 2 + 5) \sqrt{3} \} }} \\  \\  = { \rm{x {y}^{ \frac{3}{2} }  \times 9 \sqrt{3} }} \\  \\  = { \boxed{ \rm{9x \sqrt{3 {y}^{3} } }}}

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