Write sqrt(-72) in simplest radical form. Answer:

Express as product: First, we express sqrt(-72) as the product of square roots and sqrt(-1). sqrt(-72) = sqrt(-1 * 72) = sqrt(-1) * sqrt(72)Simplify sqrt(72): Next, we simplify sqrt(72) by finding the largest square factor of 72. The largest square factor of 72 is 36, which is 6^2. So we can write sqrt(72) as sqrt(36 * 2). sqrt(72) = sqrt(36 * 2) = sqrt(36) * sqrt(2) = 6 * sqrt(2)Express as i: Now, we express sqrt(-1) as the imaginary unit i. sqrt(-1) = iCombine results: Finally, we combine the results from the previous steps to write sqrt(-72) in simplest radical form as a complex number. sqrt(-72) = sqrt(-1) * sqrt(72) = i * 6 * sqrt(2) = 6i * sqrt(2) = 6i sqrt(2)

Home

Math Problems

Algebra 2

Introduction to complex numbers

Full solution

Q. Write

\sqrt{-72}

in simplest radical form.

\newline

Answer:

Express as product: First, we express $\sqrt{-72}$ as the product of square roots and $\sqrt{-1}$ . $\sqrt{-72} = \sqrt{-1 \times 72} = \sqrt{-1} \times \sqrt{72}$
Simplify $\sqrt{72}$ : Next, we simplify $\sqrt{72}$ by finding the largest square factor of $72$ . The largest square factor of $72$ is $36$ , which is $6^2$ . So we can write $\sqrt{72}$ as $\sqrt{36 \times 2}$ . $\sqrt{72}$ = $\sqrt{36 \times 2}$ = $\sqrt{72}$ $0$ $\sqrt{72}$ $1$ $\sqrt{72}$ $2$ = $\sqrt{72}$ $3$
Express as i: Now, we express $\sqrt{-1}$ as the imaginary unit $i$ . $\newline$ $\sqrt{-1} = i$
Combine results: Finally, we combine the results from the previous steps to write $\sqrt{-72}$ in simplest radical form as a complex number. $\sqrt{-72}$ = $\sqrt{-1}$ $\cdot$ $\sqrt{72}$ = $i$ $\cdot$ $6$ $\cdot$ $\sqrt{2}$ = $\sqrt{-72}$ $0$ $\cdot$ $\sqrt{2}$ = $\sqrt{-72}$ $3$