Square Root of 243

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Square root 243 can be calculated by writing the number 243 in its lowest terms. This implies that 243 can be split into its prime factors and then can be simplified further. Square root of 243 is represented as √243 and it can also be written in terms of its prime factors as √243 = √(3 * 3 * 3 * 3 * 3). Now we should pull out the numbers which are repeating twice together. This gives, √243 = 3 * 3 * √3 and hence √243= 9√3.

Example 1: Find the value of the expression, √12 + √243.

Here each square root radical should be simplified further.

√12 = √(2 * 2 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: 12 = 2√3 and similarly243 = 9√3.

So, √12 + √243 = 2√3 + 9√3 = (2 + 9) √3 = 11√3.

(Since they have the same radical √3, hence they are like terms and can be added).

Hence the value of the expression, √12+ √243 is = 11√3.
 
Example 2: Find the value of the expression, √243 - √48.

Here each square root radical should be simplified further.

√48 = √(2 * 2 * 2 * 2 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: 48 = 2* 2* √3 = 4√3 and similarly 243 = 9√3.

So, √243 - √48 = 9√3 -4√3 = (9 - 4) √3 = 5√3.

(Since they have the same radical √3, hence they are like terms and can be subtracted).

Hence the value of the expression, √243- √48 is = 5√3.

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