What is the difference between squaring $\sqrt{x - 1}$ $sqrt(x-1)$ and $\sqrt{x} - 1$ $sqrtx -1$ ?

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What is the difference between squaring $\sqrt{x - 1}$ $sqrt(x-1)$ and $\sqrt{x} - 1$ $sqrtx -1$ ?

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Answer 1 · 2016-12-22T12:42:47

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

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

Explanation:

Notice that $\sqrt{x - 1}$ $sqrt(x-1)$ is a single term, whereas $\sqrt{x} - 1$ $sqrt(x)-1$ has two terms. When we square $\sqrt{x} - 1$ $sqrt(x)-1$ , then, we need to use the distributive property when multiplying, unlike when squaring $\sqrt{x - 1}$ $sqrt(x-1)$ .

${(\sqrt{x - 1})}^{2} = \sqrt{x - 1} \cdot \sqrt{x - 1} = x - 1$ $(sqrt(x-1))^2 = sqrt(x-1)*sqrt(x-1) = x-1$

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

$= \sqrt{x} \cdot \sqrt{x} + \sqrt{x} \cdot (- 1) + (- 1) \cdot \sqrt{x} + (- 1) (- 1)$ $= sqrt(x) * sqrt(x)+sqrt(x)*(-1)+(-1)*sqrt(x)+(-1)(-1)$

$= x - 2 \sqrt{x} + 1$ $=x-2sqrt(x)+1$

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What is the difference between squaring $\sqrt{x - 1}$ $sqrt(x-1)$ and $\sqrt{x} - 1$ $sqrtx -1$ ?

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Explanation:

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