√(3x(5y + 7z)) + √(5y(7z + 3x)) + √(7z(3x + 5y))

asked by guest
on Nov 22, 2024 at 12:05 pm



You asked:

Evaluate the expression: \(\sqrt{3 \cdot x \cdot \left(5 y + 7 z\right)} + \sqrt{5 \cdot y \cdot \left(7 z + 3 x\right)} + \sqrt{7 \cdot z \cdot \left(3 x + 5 y\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \sqrt{3 \cdot x \cdot \left(5 y + 7 z\right)} + \sqrt{5 \cdot y \cdot \left(7 z + 3 x\right)} + \sqrt{7 \cdot z \cdot \left(3 x + 5 y\right)} = \sqrt{3} \sqrt{x \left(5 y + 7 z\right)} + \sqrt{5} \sqrt{y \left(3 x + 7 z\right)} + \sqrt{7} \sqrt{z \left(3 x + 5 y\right)} \)

Expanded

\[\sqrt{3 \cdot x \cdot \left(5 y + 7 z\right)} + \sqrt{5 \cdot y \cdot \left(7 z + 3 x\right)} + \sqrt{7 \cdot z \cdot \left(3 x + 5 y\right)} = \sqrt{15 x y + 21 x z} + \sqrt{15 x y + 35 y z} + \sqrt{21 x z + 35 y z}\]

Factored

\[\sqrt{3 \cdot x \cdot \left(5 y + 7 z\right)} + \sqrt{5 \cdot y \cdot \left(7 z + 3 x\right)} + \sqrt{7 \cdot z \cdot \left(3 x + 5 y\right)} = \sqrt{5} \sqrt{3 x y + 7 y z} + \sqrt{3} \sqrt{5 x y + 7 x z} + \sqrt{7} \sqrt{3 x z + 5 y z}\]

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