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A Review of Radicals

TRY IT:

sqrt(-1) sqrt(1) cube root of 0 cube root of -64 4th root of 81 sqrt(81) sqrt(-4)

OK, now here's something math people can get really picky about:

sqrt( x^2 ) = ?

What goes in here?

( )^2 = ( )( ) = x^2

Is it just x?

The answer is... sometimes.

Check it out:

What if x = 3?

sqrt( (3)^2 ) = sqrt(9) = 3

Yeah, that works.

What if x = -3?

sqrt( (-3)^2 ) = sqrt(9) = 3
Not the same!

So, it doesn't work when x is negative!

Technically,

sqrt( x^2 ) = x only when x is greater or equal to 0

If x is less than 0, we'd say

sqrt( x^2 ) = absolute value of x

Look again at our example:

 sqrt( (-3)^2 ) = abs(-3) = 3

Yep, it works!

answers