Introduction to Quadratic Surds

$\sqrt{2}+3\sqrt{5}$ is a compound surd

State the following is compound or conjugate surd.

$\sqrt{8}+\sqrt{6}$

If the simplification of the following is $-\sqrt{k}$ then find the value of $k$.

$\sqrt{20}-\sqrt{45}$

Simplify:

$\left(\sqrt{5}+\sqrt{3}\right)\left[\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}}-\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}\right]$

Simplify:

$\frac{\sqrt{2}\left(2+\sqrt{3}\right)}{\sqrt{3}\left(\sqrt{3}+1\right)}-\frac{\sqrt{2}\left(2-\sqrt{3}\right)}{\sqrt{3}\left(\sqrt{3}-1\right)}$

Simplify:

$\left(\sqrt{6}+\sqrt{10}-\sqrt{21}-\sqrt{35}\right)\left(\sqrt{6}-\sqrt{10}+\sqrt{21}-\sqrt{35}\right)$

Express the following as like surds:

$\sqrt{8},\sqrt{18},\sqrt{32},\sqrt{50}$

State the following as like or unlike.

$\sqrt{8},\sqrt{12} \text{and} \sqrt{20}$

State whether the following surds are like or unlike.

$\sqrt{60} \text{and} \sqrt{80}$

If the simplified form of $\sqrt{18}+\sqrt{50}$ is $a\sqrt{b}$, then find the value of $a+b$.

Is $\sqrt{32}+5\sqrt{2}$ an example of compound surd? (yes/no)

The algebraic sum of two or more simple surds is called a _____ surd.

$\sqrt{37}+\sqrt{5}-\sqrt{2}$ is 

The compound surd from the following surds is

State the following is compound or mixed surds.

$\frac{4}{3}\sqrt{8}+\sqrt{6} \text{and} \frac{4}{3}\sqrt{8}+\sqrt{6}$

Are $\sqrt{35}+\sqrt{2} \text{and} \sqrt{35}-\sqrt{2}$ an example of conjugate surds? (yes/no)

_____ surds are also known as complementary surds. (Conjugate/mixed/binomial)

$\sqrt{37}+\sqrt{5} \text{and} \sqrt{37}-\sqrt{5}$ are

The conjugate surd of $\sqrt{5}+\sqrt{3}$ is

State the following is monomial or binomial surd.

$\frac{4}{3}\sqrt{8}+\sqrt{6}$