Nested Surds
For each of the statements provided below, determine which non-negative values of $a$, $b$, $c$, and $d$, if any, make the equation true.
These can be attempted in any order but you might find that some statements can help inform your decisions about others.
d) $a\sqrt{b}=\sqrt{ab}$
h) $\dfrac{\sqrt{a}+b}{\sqrt{c}+d}=(\sqrt{a}+b)(\sqrt{c}-d)$
i) $\sqrt{5+2\sqrt{6}}=\sqrt{a}+\sqrt{b}$
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.
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