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