What is the perfect square of root 500?

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Answer 1 · 2018-06-22T14:03:13

$= 10 \sqrt{5}$ $=10sqrt(5)$

There is not a "perfect square" of $\sqrt{500}$ $sqrt(500)$ , here is why:

$= \sqrt{500}$ $=sqrt(500)$ has the prime factors:

$= \sqrt{5 \cdot 5 \cdot 5 \cdot 2 \cdot 2}$ $=sqrt(5*5*5*2*2)$

$= \sqrt{5^{2} \cdot 5 \cdot 2^{2}}$ $=sqrt(5^2*5*2^2)$

$= 5 \cdot 2 \cdot \sqrt{5}$ $=5*2*sqrt(5)$

$= 10 \cdot \sqrt{5}$ $=10*sqrt(5)$

Since 5 is not a perfect square it cannot be removed from the radical in an exact form, i.e. $\sqrt{5}$ $sqrt5$ is an irrational number.