1Cademy - Simplifying $$\sqrt{16n^2}$$

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Example

Simplifying $\sqrt{16n^2}$

Simplify a square root whose radicand contains both a numerical perfect square and a variable squared.

$\sqrt{16n^2}$

Since $(4n)^2 = 16n^2$ , the expression $4n$ is the value whose square equals $16n^2$ . Therefore:

$\sqrt{16n^2} = 4n$

The coefficient $16$ is a perfect square ( $4^2 = 16$ ) and the variable factor $n^2$ has an even exponent, so both parts simplify cleanly: take the square root of the coefficient to get $4$ , and halve the exponent on $n$ to get $n^1 = n$ . Combining these gives $4n$ .