Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −68\sqrt{-68}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Introduction to complex numbersright chevron icon

Full solution

Q. Use the imaginary number ii to rewrite the expression below as a complex number. Simplify all radicals. −68\sqrt{-68}
  1. Split into Factors: Express −68\sqrt{-68} as the product of square roots and −1\sqrt{-1}.\newline−68=−1×68\sqrt{-68} = \sqrt{-1 \times 68}
  2. Express as Complex Number: Express −1×68\sqrt{-1 \times 68} as a complex number using ii.\newline−68=−1×68\sqrt{-68} = \sqrt{-1} \times \sqrt{68}
  3. Find Prime Factors: Simplify 68\sqrt{68} by finding the prime factors of 6868.68=2×2×1768 = 2 \times 2 \times 17
  4. Express as Square Root: Express 68\sqrt{68} as 2×2×17\sqrt{2 \times 2 \times 17}.\newline68=4×17\sqrt{68} = \sqrt{4 \times 17}
  5. Simplify Square Root: Simplify 4×17\sqrt{4 \times 17} to 2×172 \times \sqrt{17}.\newline68=2×17\sqrt{68} = 2 \times \sqrt{17}
  6. Combine Results: Combine the results to express the original expression as a complex number. −68=−1×2×17=2i×17\sqrt{-68} = \sqrt{-1} \times 2 \times \sqrt{17} = 2i \times \sqrt{17}
  7. Final Simplification: Simplify the expression to its final form. −68=2i⋅17=2i⋅17\sqrt{-68} = 2i \cdot \sqrt{17} = 2i \cdot \sqrt{17}

More problems from Introduction to complex numbers

Question
Simplify.\newline8i+6i8i + 6i\newline\newlineWrite your answer in the form a+bia + bi.
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the complex conjugate of the given number.\newline4+10i4 + 10i\newline\newlineWrite your answer in the form a+bia + bi.
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify.\newline−4i−9i\frac{{-4i}}{{-9i}}\newline\newlineWrite your simplified answer in the form a+bia + bi.
Get tutor helpright-arrow

Posted 9 months ago

Question
Combine the like terms to create an equivalent expression.\newline7k−k+19=07k-k+19=\boxed{\phantom{0}}
Get tutor helpright-arrow

Posted 1 year ago

Question
Apply the distributive property to factor out the greatest common factor.\newline9+12n= 9+12 n=
Get tutor helpright-arrow

Posted 9 months ago

Question
Solve the equation.\newline12=n−9n=□ \begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the amplitude of y=−sin⁡(8x−3)+5 y=-\sin (8 x-3)+5 ?\newlineunits
Get tutor helpright-arrow

Posted 1 year ago

Question
What is the period of\newliney=4sin⁡(−2x+7)−1 ?  y=4 \sin (-2 x+7)-1 \text { ? } \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 1 year ago

Question
3⋅(3+20i)= 3 \cdot(3+20 i)= \newlineYour answer should be a complex number in the form a+bi a+b i where a a and b b are real numbers.
Get tutor helpright-arrow

Posted 1 year ago

Question
(35−23i)+(13+25i)= (35-23 i)+(13+25 i)= \newlineExpress your answer in the form (a+bi) (a+b i) .
Get tutor helpright-arrow

Posted 1 year ago

View all (59)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant