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Find the square root of $ 1360 $ ?

Last updated date: 25th Jul 2024
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Hint: We have to find the square root of the given number. We will first prime factorize our given number and express it as a multiplication of different prime numbers. Then we will try to make the pairs of the prime factors when a given prime factors repeats twice, then we will take the remaining factors which could not become a pair and find the square root of those parts. Thus the first step is to find the simple radical form and next would be to solve that form.

Complete step-by-step answer:
We have to find the square root of $ 1360 $ . The prime factorization of the given number yields us with,
 $ 1360 = 2 \times 2 \times 2 \times 2 \times 5 \times 17 $
Now we will find the pairs in this factorization, and leave factors which cannot be paired in the square root sign,
 $ \sqrt {1360} = 4\sqrt {17 \times 5} $
 $ \sqrt {1360} = 4\sqrt {85} $
Which is the simplest radical form of the given number’s square root
now we will write the value of $ \sqrt {17} $ and $ \sqrt 5 $ , these are standard values of the square root of numbers and should be remembered,
 $ \sqrt 5 = 2.236 $ , and
 $ \sqrt {17} = 4.123 $
Putting these values in the expression,
\[\sqrt {1360} = 4\sqrt {17} \times \sqrt 5 \]
We get,
 $ \sqrt {1360} = 4 \times 4.123 \times 2.236 $
Solving this we get,
 $ \sqrt {1360} = 36.878 $
This is the final answer of the square root of the number $ 1360 $
So, the correct answer is “36.878”.

Note: The standard values of the square root of the numbers from $ 1 $ to $ 30 $ should be remembered and also we could have calculated the square root with the long division method after turning it into the simplest radical form. The long division method, if used without simplifying the number and changing it into radical form, would become very cumbersome.