Square Root of 144

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Square root of 144 can also be represented using the square root radical sign as √144 and it can simplified further by splitting it into its prime factors. √144 can also be written as √(2 * 2 * 2 * 2 * 3 * 3) and the number which is multiplied to itself is pulled outside. This implies we get, 2 * 2 * 3 outside and it is equal to 12. Therefore, square root of 144 √144 = 12 and ‘144’ is a perfect square since its square root gives a perfect number.

Example 1: Find the value of the expression, √25 * √144.

Here each square root radical should be simplified further.

√25 = √(5 * 5). Now pull out the number which is repeating twice inside the radical.

This gives: 25 = 5 and 25’ is a perfect square since its square root gives a perfect number!

And we already have 144 = 12.

So, √25 * √144 = 5 * 12 = 60.

Hence the value of the expression, √25 * √144is = 60.
 
Example 2: Find the value of the expression, √18 * √144.

Here each square root radical should be simplified further.

√18 = √(2 * 3 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: √18 = 3√2 and here ‘18’ is a not a perfect square since its square root gives a number in the radical.

And,144 = 12.

So, √18 * √144 = 3√2 * 12 = 36√2.

Hence the value of the expression, √18 * √144 is = 36√2.
 
 
 

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