# Find the square root of $ 1360 $ ?

Last updated date: 30th Mar 2023

•

Total views: 206.7k

•

Views today: 4.83k

Answer

Verified

206.7k+ views

**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.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?