# Square Root of 1296

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In order to find the square root of a given number, we should write the given number in terms of its prime factors. The square root of 1296, represented as √1296 can be written in terms of its prime factors as = √(2* 2* 2* 2* 3* 3* 3* 3). Now the numberswhich are repeating twice inside are pulled outside and hence we get 2* 2* 3* 3 = 36. Therefore the √1296 = 36 and since we get a perfect number, hence 1296 is a perfect square.

Example 1:Find the value of the given expression: √4 * √1296.

Here each square root radical should be simplified further.

√4= √(2 * 2). Now pull out the number which is repeating twice inside the radical.

This gives: 4 = 2 and ‘4’ is a perfect square since its square root gives a perfect number!

And we already have 1296 = 36.

So, √4 * √1296 = 2 * 36 = 72.

Hence the value of the expression,√4 * √1296 is = 72.

Example 2: Find the value of the given expression: √9 * √1296.

Here each square root radical should be simplified further.

√9 = √(3 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: √9 = 3and here‘9’ is a perfect square.

We have, 1296 = 36.

So now multiplying the two radicals we get: √9 * √1296 = 3 * 36 = 108.

Hence the value of the expression, √9 * √1296 is = 108.