What is square root 73 in its simplest form?

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Answer 1 · 2017-12-29T23:24:57

$= sqrt(73)$

This question will require the idea of prime factorisations

Every natual number can be written as a product of prime numbers

Example:

$24 = color(blue)(2 * 12) = color(green)(2 * 3 * 4) = color(purple)(2 * 3 * 2 * 2 = color(red)(2^3 * 3$

$=> 24 = 2^3 * 3$ This is the prime factorisation...

So $sqrt(24) = sqrt(2^3 * 3 ) = sqrt(2^2 * 2 * 3 )= sqrt(2^2) * sqrt(2) * sqrt(3)$

$=> sqrt(24) = 2 * sqrt(2) * sqrt(3) = 2sqrt(6)$

Using our knowledge of: $sqrt(a*b) = sqrt(a) * sqrt(b)$

We know $73 = 73 * 1$ - its prime!

$sqrt(73) = sqrt(1)*sqrt(73) = sqrt(73)$

This can not be reduced any more, $sqrt(73)$ is in simplest form

$sqrt(p)$ in its simpelst form if $p$ is a prime number