MediumMathematicsHigh School (9–10)GeneralNumber Systems › Rational and Irrational Numbers Number Systems › Exponents and RadicalsNumerical

Expand and simplify (√7 + √3)² and (2√2 - 1)².

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Expand and simplify $(\sqrt{7} + \sqrt{3})^2$ and $(2\sqrt{2} - 1)^2$ .

Need a reminder? The key ideaShow

Rational plus irrational is irrational, while two irrational numbers can give either kind. $\sqrt{a}\,\sqrt{b} = \sqrt{ab}$ , but $\sqrt{a} + \sqrt{b} \neq \sqrt{a + b}$ . $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a - b$ and $(\sqrt{a} + \sqrt{b})^2 = a + b + 2\sqrt{ab}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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