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General
Easy

Question

Identify, which of the following numbers are rational or irrational.negative square root of 36

hintHint:

Hint:  
If the number under the square root is a perfect square of any integer, then the square root can be considered a rational number.
 

The correct answer is: YES an rational number.


    Let’s say x =negative square root of 36
    Step 1 of 3:
    Let’s factorise the number inside the square root i.e 36
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 36 equals 2 cross times 2 cross times 3 cross times 3 end cell row cell 36 equals 6 cross times 6 end cell row cell 36 equals 6 squared end cell end table
    Step 2 of 3:
    Put the factorised in the square root
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals negative square root of 6 squared end root end cell row cell x equals plus-or-minus 6 end cell end table
    Step 3 of 3:
    Now the can also be written as
    x equals plus 6 over 1 text  or  end text minus 6 over 1
    x is in the form of p/q.
    Final Answer:
    Hence, x can be represented in p/q form. Hence, negative square root of 36is a rational number.

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