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√(((2 - 4/7 - 3/14)·(- 7/17) + (3/2)^2)/(1 + 3/4))=

=√((17/14·(- 7/17) + 9/4)/(7/4))=

=√((- 1/2 + 9/4)/(7/4))=

=√(7/4/(7/4)) = √1 = 1

√(17/14·(- 7/17) + 9/4)/(7/4))

√(- 1/2 + 9/4)/(7/4)

√7/4*4/7

√1

1

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$\small \sqrt{\left[\left(2-\dfrac{4}{7}-\dfrac{3}{14}\right)·\left(-\dfrac{7}{17}\right)+\left(\dfrac{3}{2}\right)^2\right] : \left(1+\dfrac{3}{4}\right)} =$

$\small =\sqrt{\left[\left(\dfrac{28-8-3}{14}\right)·\left(-\dfrac{7}{17}\right)+\dfrac{9}{4}\right] : \left(\dfrac{4+3}{4}\right)} =$

$\small =\sqrt{\left[\dfrac{\cancel{17}^1}{\cancel{14}_2}·\left(-\dfrac{\cancel7^1}{\cancel{17}_1}\right)+\dfrac{9}{4}\right] : \dfrac{7}{4}} =$

$\small =\sqrt{\left[\dfrac{1}{2}·\left(-\dfrac{1}{1}\right)+\dfrac{9}{4}\right]·\dfrac{4}{7}} =$

$\small =\sqrt{\left[-\dfrac{1}{2}+\dfrac{9}{4}\right]·\dfrac{4}{7}} =$

$\small =\sqrt{\left[\dfrac{-2+9}{4}\right]·\dfrac{4}{7}} =$

$\small =\sqrt{\dfrac{\cancel7^1}{\cancel4_1}·\dfrac{\cancel4^1}{\cancel7_1}} =$

$\small =\sqrt{\dfrac{1}{1}·\dfrac{1}{1}} =$

$\small =\sqrt{1} = 1$