Question

find the square root of 529 by prime factorization method

Answer 1

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Answer:

√529=23





202=400and302=900

529 lies between 400and900

so √529 will lie between 20and30

Now look at the last digit ...9
There are only two numbers whose squares end with a 9,

3and7→ 32=9and72=49

So the possibilities are 23and27

However, 252=625and529 is less than 625

My first guess would therefore be 23

Multiplying confirms that 23×23=529

Hence √529=23


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