Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-90)=+-◻

Expressing square roots: Next, we can express the square root of -1 as i and the square root of 90 as the product of its prime factors under the radical. ±sqrt(-1 * 90) = ±i * sqrt(90)Simplifying square root of 90: Now, we simplify the square root of 90 by finding the prime factors of 90 and identifying any perfect squares. 90 = 2 * 45 45 = 5 * 9 9 is a perfect square (3^2), so we can take the square root of 9 out of the radical. ±i * sqrt(90) = ±i * sqrt(2 * 5 * 9)Taking square root of 9 out: We can now simplify the expression by taking the square root of 9 out of the radical, which is 3. ±i * sqrt(2 * 5 * 9) = ±i * 3 * sqrt(2 * 5)Combining constants outside radical: Finally, we simplify the expression by combining the constants outside the radical. ±i * 3 * sqrt(2 * 5) = ±3i * sqrt(10)

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Algebra 2

Introduction to complex numbers

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Q. Express the radical using the imaginary unit,

i

\newline

Express your answer in simplified form.

\newline

\pm \sqrt{-90}= \pm \square

Expressing square roots: Next, we can express the square root of $-1$ as $i$ and the square root of $90$ as the product of its prime factors under the radical. $\pm\sqrt{-1 \times 90} = \pm i \times \sqrt{90}$
Simplifying square root of $90$ : Now, we simplify the square root of $90$ by finding the prime factors of $90$ and identifying any perfect squares. $\newline$ $90 = 2 \times 45$ $\newline$ $45 = 5 \times 9$ $\newline$ $9$ is a perfect square $(3^2)$ , so we can take the square root of $9$ out of the radical. $\newline$ $\pm i \times \sqrt{90} = \pm i \times \sqrt{2 \times 5 \times 9}$
Taking square root of $9$ out: We can now simplify the expression by taking the square root of $9$ out of the radical, which is $3$ . $\newline$ $\pm i \cdot \sqrt{2 \cdot 5 \cdot 9} = \pm i \cdot 3 \cdot \sqrt{2 \cdot 5}$
Combining constants outside radical: Finally, we simplify the expression by combining the constants outside the radical. $\pm i \times 3 \times \sqrt{2 \times 5} = \pm 3i \times \sqrt{10}$