square root of 2250 by factoring and finding pairs

Question

Find the square root of 2250 by finding pairs

Answer 1

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sqrt(2250)=47.4341649025257...

Answer 2

2250=2*3^2*5^3. So the pairs are 3^2 and 5^2, leaving unmatched pairs 2 and 5, allowing us to take the square root 3*5=15. To find the square root the number radicalises to 15sqrt(10)=13*3.1623=47.4342 (correct to 4 places of decimals).