Simplify: \(\sqrt{3+2\sqrt2}\)

1.	Simplify: \(\sqrt{3+2\sqrt2}\)
Answer» \(\sqrt{3+2\sqrt2}\) \(= \sqrt{2+1+2\sqrt2}\) \(= \sqrt{(\sqrt2)^2 + (1)^2 + 2 \times \sqrt2 \times 1}\) ^{\(= \sqrt{(\sqrt2+1)^2}\)} \(= \sqrt2+1\)

Answer»

\(\sqrt{3+2\sqrt2}\)

\(= \sqrt{2+1+2\sqrt2}\)

\(= \sqrt{(\sqrt2)^2 + (1)^2 + 2 \times \sqrt2 \times 1}\)

^{\(= \sqrt{(\sqrt2+1)^2}\)}

\(= \sqrt2+1\)

Discussion

The simplest rationalising factor of 2√5 - √3 isA. 2√5 + 3B. 2√5 + C. √5 + √3D. √5 - √3
The simplest rationalising factor of √3+ √5 isA. √3 - 5B. 3 - √5C. √3 - √5D. √3 + √5
Simplify:(√8 – √2) (√8 + √2)
Simplify each of the following:(i) \(\sqrt[3]{4}\) x \(\sqrt[3]{16}\)(ii) \(\frac{\sqrt[4]{1250}}{\sqrt[4]{2}}\)
Simplify:(3 + √3)(5 - √2)
Simplify:(3 + √3) (3 – √3)
Simplify:(4 + √7) (3 + √2)
Simplify:(√5 – √2) (√5 + √2)
Simplify:(√3 + √7)2
Simplify:(√5 – √3)2.