Question

find the square root of 361

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Answer 1

The square root of 361 is 19

Hope my answer helps

Answer 2

Answer:

The square root of 361 is 19.

Step-by-step explanation:

$361 = {19}^{2}$

, So,

$\sqrt{361}$

=19

Prime Factorisation

One of the best ways to attempt to find the square root of a whole number is to factor it into primes and identify pairs of identical factors. This is a bit tedious in the case of 361 as we shall see:

Let's try each prime in turn:

2 : No: 361 is not even.

3 : No: The sum of the digits is not a multiple of 3.

5 : No: The last digit of 361 is not 0 or 5.

7 : No: 361÷7=51 with remainder 4.

11 : No: 361÷11=32 with remainder 9.

13 : No: 361÷13=27 with remainder 10.

17 : No: 361÷17=21 with remainder 4.

19 : Yes: 361=19⋅19

So

$\sf{\bold{\red{\sqrt{361= 19} }}}$