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Simplify 12 square root five plus three square root five.
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In order to add square roots, the number inside of the root must be exactly the same as the other one inside of the square root.
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And we have that.
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They’re both square root five.
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So we will keep that square root five and we will add the numbers in front of them.
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So we will have 12 plus three and then square root five.
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And 12 plus three is equal to 15.
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This means that our answer will be 15 square root five.
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Sometimes, it’s useful to think when adding and subtracting square roots is to treat them like variables.
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Imagine this to be 12𝑥 plus three 𝑥.
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So the square root fives represent like variables.
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They’re both 𝑥s.
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They’re both square root fives.
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So 12𝑥 plus three 𝑥 is 15𝑥.
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We keep the 𝑥 just like we keep the square root five as long as they’re the same.
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So if one of the square root fives haven’t had been different, we wouldn’t have been able to combine them.
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Just like if this had been a three 𝑦, we wouldn’t be able to combine 12𝑥 and three 𝑦.
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We would simply have to leave them apart.
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So once again, our final answer will be 15 square root five.