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What is the expression in simplest radical form?

 

AngelRay  Dec 26, 2017
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Simplify the following:
sqrt(504)

Factor 504 under the radical sign.
sqrt(504) = sqrt(8×9×7) = sqrt(2^3×3^2×7):
sqrt(2^3 3^2 7)

Simplify powers.
sqrt(2^3 3^2 7) = sqrt(2^3) sqrt(3^2) sqrt(7) = 2^(3/2)×3^(2/2) sqrt(7) = 2 sqrt(2)×3 sqrt(7):
3×2 sqrt(2) sqrt(7)

Multiply 3 and 2 together.
3×2 = 6:
6 sqrt(2) sqrt(7)

For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(2) sqrt(7).
sqrt(2) sqrt(7) = sqrt(2×7):
6 sqrt(2×7)

Multiply 2 and 7 together.
2×7 = 14:
6 sqrt(14 )
 

Guest Dec 26, 2017

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