Question

The square root of a2 - 2a + 1 is
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Answer 1

Answer:

${a}^{2} - 2a + 1 \\ = {a }^{2} - a - a + 1 \\ = a(a - 1) - 1(a - 1) \\ = (a - 1) ^{2} \\ square \: root \: of \: (a - 1) ^{2} \\ = \sqrt{ {(a - 1)}^{2} } = (a - 1)$

Step-by-step explanation:

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Answer 2

Answer:

Required square root is (a-1).

Step-by-step explanation:

Given term is

${a}^{2} - 2a + 1$

Basically this is a very known formula of Algebra.

The formula is

${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} ......(1)$

Here

$x = a \: and \: y = 1$

So,From (1),

${a}^{2} - 2 \times a \times 1 + {1}^{2}$

${(a - 1)}^{2}$

Square root of

${(a - 1)}^{2}$

So,

$\sqrt{ {(a - 1)}^{2} } = \sqrt{(a - 1)(a - 1)} = (a - 1)$

Here applied formulas are

${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

$\sqrt{ {x}^{2} } = \sqrt{x \times x} = x$

Some others formula of Algebra are

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

${x}^{2} - {y}^{2} = (x + y)(x - y)$

${x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy$

e.t.c