Hi,Response previously posted

 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 square root of (486) can be simplified as follows:

it is equivalent to:

square root of (486 * 1)

or:

square root of (54 * 9)

or:

square root of (6 * 9 * 9) which is equivalent to:

square root of (6 * 9^2)

since the square root of (x^2) is equal to x, this means that:

the square root of (6 * 9^2) is equal to 9 * square root of (6)

you can use your calculator to confirm that 9 * sqrt(6) is equivalent to sqrt(486)

the square root of (864) is not equivalent to the square root of (24) plus the square root of (6).

you can also use your calculator to confirm that statement is not true.

the arithmetic laws of square roots state:

sqrt(a*b) = sqrt(a) * sqrt(b)

sqrt(a/b) = sqrt(a) / sqrt(b)

those laws do not work with addition or subtraction.

sqrt(a+b) does NOT equal sqrt(a) + sqrt(b)

sqrt(a-b) does NOT equal sqrt(a) - sqrt(b)

here's some references that might help you to refresh your memory.

http://www.themathpage.com/alg/radicals.htm

http://www.themathpage.com/alg/simplify-radicals.htm

http://www.themathpage.com/alg/multiply-radicals.htm





 

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