Evaluate (-2 square root of 3)^2

Problem

(−2⁢3)2 open paren negative 2 the square root of 3 close paren squared

Solution

  1. Apply the power of a product rule, which states that (a⁢b)n=an⁢bn open paren a b close paren to the n-th power equals a to the n-th power b to the n-th power

(−2⁢3)2=(−2)2⋅(3)2 open paren negative 2 the square root of 3 close paren squared equals open paren negative 2 close paren squared times open paren the square root of 3 close paren squared

  1. Evaluate the square of the coefficient by multiplying −2 negative 2 by itself.

(−2)2=4 open paren negative 2 close paren squared equals 4

  1. Evaluate the square of the radical by using the property (x)2=x open paren the square root of x close paren squared equals x

(3)2=3 open paren the square root of 3 close paren squared equals 3

  1. Multiply the results to find the final value.

4⋅3=12 4 times 3 equals 12

Final Answer

(−2⁢3)2=12 open paren negative 2 the square root of 3 close paren squared equals 12

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