Question

question 10 of 10
the value of \\(\sqrt{-16}\\) is not -4 because ______.

a. \\(4^2 \
eq -16\\)

b. \\((-16)^2 \
eq -4\\)

c. \\(16^2 \
eq -4\\)

d. \\((-4)^2 \
eq -16\\)

Explanation:

To determine why \(\sqrt{-16}\) is not \(-4\), we check the square of \(-4\). The square of a number \(x\) is \(x^2\). For \(x = -4\), we calculate \((-4)^2\). By the rule of squaring negative numbers, \((-4)^2=(-4)\times(-4) = 16\), which is not equal to \(-16\). Let's analyze other options: Option A: \(4^2=16
eq - 16\), but we are checking for \(-4\), so this is not relevant. Option B: \((-16)^2 = 256
eq - 4\), which is not related to the square of \(-4\). Option C: \(16^2=256
eq - 4\), also not related to the square of \(-4\). So the correct reason is that \((-4)^2
eq - 16\).

Answer:

D. \((-4)^2
eq -16\)