Square Root of 250

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Square root of 250 is written using the square root radical sign as √250 and it can be simplified further by splitting the number 250 into its prime factors. 250 is split into its prime factors as 2 * 5 * 5 * 5 which implies √250 = √(2 * 5 * 5 * 5). Now we can simplify this further by pulling out the number which is multiplied to itself. This gives √250 = 5 * √(2 * 5) = 5√10. Therefore the square root of 250 is √250 = 5√10.
 
Example 1: Find the value of the expression, √40 + √250.

Here each square root radical should be simplified further.

√40 = √(2* 2* 2* 5). Now pull out the number which is repeating twice inside the radical.

This gives: 40 = 2√(2* 5)= 2√10 and similarly 250 = 5√10.

So, √40 + √250 = 2√10 + 5√10 = (2 + 5) √10 = 7√10.

(They are like terms since they have the same radical √10 and hence can be added).

Hence the value of the expression, √40 + √250 is = 7√10.
 
Example 2: Find the value of the expression, √250 - √10.

Here each square root radical should be simplified further.

√10 = √(2* 5)and it is already in its simplified form as no number is repeating twice inside the radical to be pulled out.

And we have 250 = 5√10.

So, √250 - √10 = 5√10 -1√10 = (5 – 1) √10 = 4√10.

(They are like terms since they have the same radical √10 and hence can be added).

Hence the value of the expression, √250- √10 is = 4√10.
 
 
 
 
 

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