Sum and Difference of Square Roots - Rules & Examples
Read this topicExplanations 3
- Sums and differences can't be separated into different radicals Arithmetic under a radical works a lot like arithmetic within parentheses—which is to say, pretty normally, excep…
By Zora Gilbert, Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- You Cannot Split a Sum or Difference Under A Radical Into Two Radicals If we have a singular product or a quotient under a radical, we are able to split that original radical in…
By Alex Federspiel, Caroline K, Jonathan Heller, Anusha Rahman
- (Video) Sum of Square Roots by Art of Problem Solving This video by Art of Problem Solving talks about sum of square roots and shows why you can't split up addition under a radi…
By Alex Federspiel, Jonathan Heller, Caroline K, Anusha Rahman
Problems 20
- Which is larger? AB4+164+16\begin{array}{c|c} \text{A}&\text{B}\\ \hline \sqrt{4+16}&\sqrt{4}+\sqrt{16} \end{array}A4+16B4+16
- Which is larger? AB16−416−4\begin{array}{c|c} \text{A}&\text{B}\\ \hline \sqrt{16-4}&\sqrt{16}-\sqrt{4} \end{array}A16−4B16−4
- True or False\text{True or False}True or False === If you have two natural numbers, aaa and bbb, then a+b>a+b\sqrt{a}+\sqrt{b}>\sqrt{a+b}a+b>a+b.
- True or False\text{True or False}True or False === If you have two natural numbers, aaa and bbb, where a>ba>ba>b, then a−b>a−b\sqrt{a}-\sqrt{b}>\sqrt{a-b}a−b>a−b.
- Simplify as much as possible: 6x2+4x2−x2\sqrt{6x^2+4x^2-x^2}6x2+4x2−x2
- Simplify 9+16\sqrt{9+16}9+16
- Simplify 4+16\sqrt{4+16}4+16
- Simplify 64+36\sqrt{64+36}64+36
- Simplify 25+144\sqrt{25+144}25+144
- Simplify 81+144\sqrt{81+144}81+144
- Simplify 64+225\sqrt{64+225}64+225
- Simplify 256+144\sqrt{256+144}256+144
- Simplify 400+225\sqrt{400+225}400+225
- Simplify 400+441\sqrt{400+441}400+441
- True or False\text{True or False}True or False === Suppose aaa and bbb are perfect squares such that a+ba+ba+b is a perfect square. Then a+b=a+b\sqrt{a+b}=\sqrt{a}+\sqrt{b}a+b=…
- Simplify 25−16\sqrt{25-16}25−16
- Simplify 169−25\sqrt{169-25}169−25
- Simplify 400−256\sqrt{400-256}400−256
- Simplify 100−36\sqrt{100-36}100−36
- True or False\text{True or False}True or False === Suppose aaa and bbb are perfect squares such that a−ba-ba−b is a perfect square. Then a−b=a−b\sqrt{a-b}=\sqrt{a}-\sqrt{b}a−b=…