Add or subtract, as indicated. See Example 6.

-5√32 + 2√98

Question

Add or subtract, as indicated. See Example 6.

-5√32 + 2√98

Accepted Answer

Hey, everyone here we are asked to perform the indicated operation in the given expression negative eight, multiplied by the square root of 80 plus 10, multiplied by the square root of 405. Here we have four answer choice options, answer choice A 12 multiplied by the square root of three. Answer B 58 multiplied by the square root of five. Answer C negative 32 multiplied by the square root of three and answer D 27 multiplied by the square root of five. So before we can begin summing the two terms given in our expression, we first need to manipulate both of them so that the values underneath the square roots are the same. So we want to begin by factoring both of the values underneath the roots into their largest perfect squares. So starting with our first term again, we have negative a multiplied by the square root of A. And now factoring underneath the root, we will now have 16, multiplied by five. And now with our second term, again, we have plus 10 multiplied by the square root of 405. And now factoring 405 into its largest perfect square, we have 81 multiplied by five underneath the square root. So now we just want to begin simplifying. So first, we want to recall that the square root of 16 is four and the square root of 81 is nine. And we also want to notice that underneath both of these square roots. So far, we have the value of five. So we want to make sure we keep this value in our simplified form. So doing this, we have negative eight multiplied by the square root of 16, which simplifies 24. And then this is multiplied by the square root of five. Now, with our second term, we have plus 10 multiplied by nine, multiplied by the square root of five. And now simplifying further by multiplying the necessary values, we have negative 32 multiplied by the square root of five plus 90 multiplied by the square root of five. So now we see that for both of our terms, we both have the square root of five. And since we have the same value underneath both of the roots, we are OK to start summing the two terms. So we have negative 32 plus 90 which simplifies to 58. And so our simplified value is 58 multiplied by the square root of five. So with this value, we are left with answer choice B where after performing the indicated operation on our given expression, we are left with 58 multiplied by the square root of five. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Add or subtract, as indicated. See Example 6. -5√32 + 2√98

Key Concepts

Simplifying Radicals

Combining Like Terms

Arithmetic with Radicals

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