Add or subtract, as indicated. See Example 6.

2√50 - 5√72

Question

Add or subtract, as indicated. See Example 6.

2√50 - 5√72

Accepted Answer

Hey, everyone. Here we are asked to perform the indicated operation in the given expression, five multiplied by the square root of 112 minus seven, multiplied by the square root of 175. Here we have four answer choice options, answer choice. A 55 multiplied by the square root of seven. Answer B negative 13 multiplied by the square root of five. Answer C negative 15 multiplied by the square root of seven and answer D multiplied by the square root of five. So before we can begin subtracting our terms in the given expression, we first need to manipulate both terms so that the values underneath these square roots are the same. So beginning with our first term again, recalling we have five multiplied by the square root of 112. We now want to factor 112 into its largest perfect square. So underneath the square root, we now have 16 multiplied by seven. And now repeating this step for the second term again, recalling that we originally had minus seven multiplied by the square root of 175. Well, factoring 175 we now have underneath the square root 25 multiplied by seven. So now we just want to start simplifying further since we can notice that both square roots have the value of seven. So simplifying, we first want to recall that the square root of 16 is four and the square root of 25 is five. So now we can simplify. So first, we have five multiplied by four multiplied by the square root of the seven minus seven, multiplied by five multiplied by the square root of seven. And now we want to continue to simplify by multiplying the necessary values. So doing this, we have 20 multiplied by the square root of seven minus 35 multiplied by the square root of seven. And now we see that underneath both of our square roots, we have the same value of seven. So we can now start subtracting. So 20 minus 35 gives us negative 15, which leaves us with our final expression where we have negative 15 multiplied by the square root of seven. So with this final expression, we are left with answer choice C where again, after performing the indicated operation in our given expression, we are left with negative 15 multiplied by the square root of seven. 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. 2√50 - 5√72

Key Concepts

Simplifying Radicals

Combining Like Terms

Distributive Property

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