Square Root of One

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Square root of a number or an expression is represented by the square root radical sign ‘√’ and square root of numbers can be simplified by splitting the given number into its prime factors. However square root of one is equal to one itself and it is represented as √1 = 1. This is because ‘1’ can be expressed as 1 * 1 and hence √1 = √(1 * 1) = 1. Any number can be written in terms of ‘1’ and therefore they can also be written in terms of square root of 1.

Example 1: What is the value of the expression, √36 + √1?

Here each square root number should be simplified further.

√36= √(2 * 2 * 3 * 3). Now pull out the number which is repeating twice inside the radical.

This gives: 36= 2 * 3 = 6.

And 1 = √(1 * 1) = 1.

Now adding the above both answers, we get: √36 + √1 = 6 + 1 = 7.

Hence the value of the expression √36 + √1 = 7.
 
Example 2: What is the value of the expression, √64 + √1?

Here each square root number should be simplified further.

√64= √(2 * 2 * 2 * 2 * 2 * 2). Now pull out the number which is repeating twice inside the radical.

This gives: 64= 2 * 2 * 2 = 8

And 1 = √(1 * 1) = 1.

So, √64 + √1 = 8 + 1 = 9.

Hence the value of the expression √64 + √1 = 9.
 
 
 

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