How do you simplify $\sqrt{t} \cdot \sqrt{t}$ $sqrtt*sqrtt$ ?

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How do you simplify $\sqrt{t} \cdot \sqrt{t}$ $sqrtt*sqrtt$ ?

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Answer 1 · 2017-07-11T00:10:03

$| t |$ $|t|$

Explanation:

We can multiply these together like this:

$\sqrt{t} \cdot \sqrt{t} = \sqrt{t \cdot t} = \sqrt{t^{2}}$ $sqrtt * sqrtt = sqrt(t*t) = sqrt(t^2)$

You might feel inclined to say that $\sqrt{t^{2}} = t$ $sqrt(t^2) = t$ , but notice that if $t$ $t$ is negative, $t^{2}$ $t^2$ is still positive, and so the square root of $t^{2}$ $t^2$ will be positive $-$ $-$ that is, the absolute value of $t$ $t$ .

No matter what, $\sqrt{t^{2}}$ $sqrt(t^2)$ will always be positive (or $0$ $0$ ) since any number squared is non-negative. Therefore, we can say that:

$\sqrt{t} \cdot \sqrt{t} = \sqrt{t^{2}} = | t |$ $sqrtt * sqrtt = sqrt(t^2) = |t|$

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How do you simplify $\sqrt{t} \cdot \sqrt{t}$ $sqrtt*sqrtt$ ?

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