Basic Concept Of Radical

Algebra Level 1

True or false:

\quad For all real x x , x 2 = x \sqrt{ x^2 } = x .

True False

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2 solutions

Matheus Henrique
Apr 3, 2016

The square root of 16 is also MINUS 4. And so 'minus 4' DOES equal 'minus 4'. The question is ambiguous.

Steven Bennett - 5 years, 1 month ago

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Hi Steven, the square root function is defined such that it returns the positive value only. Thus ( 4 ) 2 = ( 4 ) 2 = 4 \sqrt{(4)^2} = \sqrt{(-4)^2} = 4 and not 4 -4 . Please go through this wiki for more details:

Does a square root have two values?

Pranshu Gaba - 5 years, 1 month ago

Root x^2 does not equal to x, for all of x is an element of real numbers. Root x^2 equals to the absolute value of x, for all of x is an element of real numbers. For anybody who doesn't know what it means (me at first, haha).

Rico Lee - 5 years, 2 months ago

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Hahaha yes, I'm sorry but I didn't speak English fluently, so I don't know how to write some complex Math terms. Because that I prefer write in the "universal way". I'm Brazillian, sorry for the English :)

Matheus Henrique - 5 years, 2 months ago

Ur thinking bout it all wrong. Ur making it too complicated

Ben Hunter - 5 years, 1 month ago

Are there not always to answers of a squareroot. You are going to get both a positive and negativ answer.

Lars Stutzer - 5 years, 1 month ago

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Hi Lars, the square root function is defined such that it returns the positive value only. Thus ( 4 ) 2 = ( 4 ) 2 = 4 \sqrt{(4)^2} = \sqrt{(-4)^2} = 4 and not 4 -4 . Please go through this wiki for more details:

Does a square root have two values?

Pranshu Gaba - 5 years, 1 month ago

assume that x = -2 , then x^2 = 4 ,sqrt(4) = 2 - therefore -2 not equal 2

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