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Example

Simplifying 25\sqrt{25}, 121\sqrt{121}, and 144-\sqrt{144}

To simplify square roots without variables, identify the counting number whose square equals the radicand, and apply the appropriate sign:

25\sqrt{25}: Since 52=255^2 = 25, the number 55 is the positive value whose square equals 2525. Therefore, 25=5\sqrt{25} = 5.

121\sqrt{121}: Since 112=12111^2 = 121, the number 1111 is the positive value whose square equals 121121. Therefore, 121=11\sqrt{121} = 11.

144-\sqrt{144}: First, evaluate the principal square root. Since 122=14412^2 = 144, 144=12\sqrt{144} = 12. The negative sign in front of the radical instructs us to take the opposite of the principal square root. Therefore, 144=12-\sqrt{144} = -12.

Familiarity with perfect squares makes this process quick and straightforward.

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Updated 2026-04-21

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