In Exercises 11–28, add or subtract as indicated. You will need t...

Question

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals.
_ __
√5 + √20

Accepted Answer

Hey, everyone in this problem, we're asked to perform the addition of radicals. After simplification, the expression we're given is the square root of seven plus the square root of 63. We're given four answer choices. Option A two multiplied by the square root of seven. Option B four multiplied by the square root of seven. Option C, the square root of seven plus seven multiplied by the square root of three. And option D, the square root of 7 -7 multiplied by the square root of three. We're gonna start by rewriting what we were getting. We have the square root of seven plus the square root of 63. Now, the square root of seven, we can't simplify any further. OK. Seven is a prime number is we can't break it up into separate factors and the square root of seven is not a nice integer value. And so the square root of seven, we're gonna have to leave alone, then we moved to the square root of 63. OK. Let's try to break 63 up into two factors. They were one of them is able to get a nice square root. OK? We can take the square root and get an integer. So 63, well, we can write this as nine multiplied by seven. And we know the square root of nine is three. And then we're left with the squared of seven and again, seven is a prime number. So it can't be simplified further. Now, we've broken up 63 into these factors underneath the square root. But how do we actually apply the square root? We recall that if we have the square root of two things multiplied together, say the square root of X multiplied by Y, we can write this as the square root of X multiplied by the square root of Y. So we can break it up, take the square root of each of those factors individually and then multiply the result together. So our expression is going to be equal to the square root of seven plus the square root of nine multiplied by the square root of seven and the square root of nine is equal to three. And so we get the square root of seven plus three multiplied by the square root of seven, the square root of 7-plus 3 multiplied by the square root of seven. Well, that's equal to four multiplied by the square root of seven. And so we were able to simplify our two radicals, our two square roots down to a single square root with a constant coefficient in front. We found the co the correct answer is four multiplied by the square root of seven which corresponds with answer choice B. That's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20

Key Concepts

Radicals

Like Radicals

Simplification of Radicals

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