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What is √2323 in simplest form as a radicand and a number outside the radicand

User Solar
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1 Answer

3 votes

Since 2323 = 23*101 has no perfect square factors, this means we cannot simplify
\sqrt{2323 into the form
a√(b)

It seems like your teacher may have made a typo. I would double check with them.

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I'll show you how to simplify a different problem. Let's say we want to simplify
√(232)

Find the prime factorization of the radicand:

232 = 2^3*29

we can rewrite the "2^3" as "2^2*2" to pull out the perfect square factor, which helps us simplify as such:


√(232) = √(2^3*29)


√(232) = √(2^2*2*29)


√(232) = √(2^2*58)


√(232) = √(2^2)*√(58)


√(232) = 2*√(58)

For the last two steps I used these square root rules


√(x*y) = √(x)*√(y)


√(x^2) = x where x is nonnegative

User Seva
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