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How do you find the square root of 338?

Answer
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Hint:
Here we must know what square root actually means. Square root of any number means we need to find the number which when multiplied by itself gives us the number inside the root. Similarly here we need to find the number which when multiplied by itself gives us 338.

Complete step by step solution:
Here we are given to find the square root of338
We must know that when we are asked to find the square root of any number we actually need to find the number which when multiplied by itself gives us that number present inside the root. Here we need to find the number which gives us 338 when multiplied by itself. The example will make it clearer. If we need to find the square root of the number 9 so need to find the number which when multiplied by itself gives us the number 9
We know that 3×3=9 so its answer is 3 as when 3 is multiplied by itself the result is 9
Similarly we need to find the square root of the term 338 which can be written as 338
So we need to know that:
338=(2)(169)169=(13)(13)13=(13)((1)
From the above factors of 40 we get to know that we can write 40 in the form of its factors as:
338=(2)(13)(13)
So we need to find the value of 338=(2)(13)(13)
In such problems where we have terms inside the root, we must know that if the same term inside the root is occurring twice, we can write it once outside the root.
As here we can see that one pair can be made of the numbers 13 which is inside the root and one (2) will be left inside. So we can take the number that is in pair outside the root and we will get:
338=(2)(13)(13)=132
We also know that approximate value of 2=1.414
So we can simplify it further as:
13(1.414)=18.382

So we get that 338=132=18.382

Note:
Here if we would have been given to find the square of 132 then we would have multiplied it twice and then we would have written the answer which would be 338 and therefore the student must know the difference between square of the number and square root of the number.
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