Learn Before
Example

Simplifying 36\sqrt{36}, 196\sqrt{196}, 81-\sqrt{81}, and 289-\sqrt{289}

Simplify each expression by recognizing the radicand as a perfect square and, when a negative sign appears in front of the radical, applying it after evaluating the principal square root.

36=6\sqrt{36} = 6: Since 62=366^2 = 36, the principal square root of 3636 is 66.

196=14\sqrt{196} = 14: Since 142=19614^2 = 196, the principal square root of 196196 is 1414.

81=9-\sqrt{81} = -9: The negative sign sits in front of the radical, not under it. Evaluate the principal square root first: 81=9\sqrt{81} = 9 because 92=819^2 = 81. Then apply the negation to obtain 9-9.

289=17-\sqrt{289} = -17: Again, the negative sign is placed before the radical. Evaluate the square root first: 289=17\sqrt{289} = 17 because 172=28917^2 = 289. Then apply the negation to obtain 17-17.

Parts ⓐ and ⓑ are straightforward evaluations of the principal square root. Parts ⓒ and ⓓ reinforce that a negative sign in front of the radical means "take the opposite of the principal square root" — the negation is applied only after the square root has been computed.

0

1

Updated 2026-04-21

Contributors are:

Who are from:

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Related
Learn After