What is the Square root of 21?

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What is the Square root of 21?

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Answer 1 · 2015-10-17T11:31:20

$21 = 3 \cdot 7$ $21 = 3*7$ has no square factors, so $\sqrt{21}$ $sqrt(21)$ cannot be simplified.

$\sqrt{21} \approx 4.58257569495584000658$ $sqrt(21) ~~ 4.58257569495584000658$ is an irrational number whose square is $21$ $21$ .

Explanation:

$\sqrt{21} = \sqrt{3 \cdot 7}$ $sqrt(21) = sqrt(3*7)$ has no square factors that can be 'moved outside the square root sign'.

For example $\sqrt{12} = \sqrt{2^{2} \cdot 3} = \sqrt{2^{2}} \sqrt{3} = 2 \sqrt{3}$ $sqrt(12) = sqrt(2^2*3) = sqrt(2^2)sqrt(3) = 2sqrt(3)$

So $\sqrt{21}$ $sqrt(21)$ cannot be simplified.

It cannot be expressed as a rational number (fraction), so the best we can do with normal notation is to either stick with $\sqrt{21}$ $sqrt(21)$ or give an approximation, such as $\sqrt{21} \approx 4.58$ $sqrt(21) ~~ 4.58$ .

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What is the Square root of 21?

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