Question

Which one of the following is a compound surd?

• A. $\sqrt[2]{212}+\sqrt[2]{227}+\sqrt[2]{248}$
• B. $\sqrt[2]{248}+\sqrt[2]{280}+\sqrt[2]{220}$
• C. 2$\times \sqrt[2]{272}+3\times \sqrt[2]{232}$
• D. 5$\times \sqrt[2]{220}+2\times \sqrt[2]{245}+\sqrt[2]{280}$

Answer 1

The correct option is B

$\sqrt[2]{248}+\sqrt[2]{280}+\sqrt[2]{220}$

$\sqrt[2]{212}+\sqrt[2]{227}+\sqrt[2]{248}=\sqrt[2]{2\left(4\right)\left(3\right)}+\sqrt[2]{2\left(9\right)\left(3\right)}+\sqrt[2]{2\left(16\right)\left(3\right)}=2\sqrt[2]{23}+3\sqrt[2]{23}+4\sqrt[2]{23}=9\sqrt[2]{23}$ - simple surds

2$\sqrt[2]{248}+3\sqrt[2]{280}+4\sqrt[2]{220}=2\sqrt[2]{2\left(16\right)\left(3\right)}+3\sqrt[2]{2\left(16\right)\left(5\right)}+4\sqrt[2]{2\left(4\right)\left(5\right)}=8\sqrt[2]{23}+12\sqrt[2]{25}+8\sqrt[2]{25}=20\sqrt[2]{25}+8\sqrt[2]{23}$ - compound surds

2$\sqrt[2]{272}+3\sqrt[2]{232}+4\sqrt[2]{250}=2\sqrt[2]{2\left(36\right)\left(2\right)}+3\sqrt[2]{2\left(16\right)\left(2\right)}+4\sqrt[2]{2\left(25\right)\left(2\right)}=12\sqrt[2]{22}+12\sqrt[2]{22}+20\sqrt[2]{22}=44\sqrt[2]{23}$ - simple surds

5$\sqrt[2]{220}+4\sqrt[2]{245}+\sqrt[2]{280}=5\sqrt[2]{2\left(4\right)\left(5\right)}+4\sqrt[2]{2\left(9\right)\left(5\right)}+\sqrt[2]{2\left(16\right)\left(5\right)}=10\sqrt[2]{25}+12\sqrt[2]{25}+4\sqrt[2]{25}=26\sqrt[2]{25}$ - simple surds