In Exercises 1–10, perform the indicated operations and write the...

Question

In Exercises 1–10, perform the indicated operations and write the result in standard form.
        __
4 + √−8  /  2

Accepted Answer

Hey, everyone. Here we are asked to simplify the following expression and express the answer in standard form. If necessary. Here we are given the expression 39 plus the square root of negative 507 all divided by 13. Here we have four answer choice options, answer choice. A one third minus the square root of three divided by three multiplied by I answer B one third plus the square root of three divided by three multiplied by I answer C three minus the square root of three multiplied by I and answer D three plus the square root of three multiplied by I. So looking at our given expression, we can first notice that in the numerator we have the sum of two terms. So our first step in simplifying is to just break up our fraction into two different fractions. So doing this, we have 39 divided by 13 plus the square root of negative 507 divided by 13. And so now here we can see that we can make an immediate simplification if we notice that 39 divided by 13 simplifies to just three. So we have three plus our second fraction here where uh in the numerator, we have again, the square root of negative 507. Well, first, we want to break up this 507 into its largest perfect square. Well, the largest perfect square of 507 is 169. So now underneath the square root, we have 169 multiplied by negative three. And this is still divided by 13. And so now we can start simplifying the values underneath the square root. So again, we have three plus and now the square root of 169 is 13. So we have 13 multiplied by the square root of negative three. And this is still divided by 13. And now we see that we have a 13 in the numerator and the denominator. So they cancel each other out. And now rewriting we have three plus the square root of negative three. And now we can break up the negative three. So we have three plus the square root of three times negative one. And so now we just need to recall that the square root of negative one is I. So now just rewriting using I, we have three plus the square root of three multiplied by I. And now with our simplified form, we are left with answer choice D where again, we have three plus the square root of three multiplied by I. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 1–10, perform the indicated operations and write the result in standard form. __ 4 + √−8 / 2

Key Concepts

Complex Numbers

Standard Form of Complex Numbers

Operations with Complex Numbers

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