Operations with surds

Adding and subtracting like surds, multiplying and dividing surds, and simplifying first to combine.

Adding and subtracting

Only like surds (same number under the root) can be combined, just like like terms: $3\sqrt{2} + 5\sqrt{2} = 8\sqrt{2}$. Simplify first to find hidden like surds.

Example 1●●

Simplify $\sqrt{18} + \sqrt{8}$.

$3\sqrt{2} + 2\sqrt{2}$

$= 5\sqrt{2}$

Multiplying and dividing

Example 2●●

Simplify $2\sqrt{3} \times 4\sqrt{2}$.

$(2 \times 4)\sqrt{3 \times 2} = 8\sqrt{6}$

Flashcards

$sqrt{3} imes sqrt{5}$

$\sqrt{15}$

$(sqrt{7})^2$

$7$

$sqrt{20} div sqrt{5}$

$2$

Practice

Simplify $\sqrt{18} + \sqrt{8}$. Type a surd like 5sqrt(2) or 5√2.
Simplify $2\sqrt{3} \times 4\sqrt{2}$.
Simplify $3\sqrt{2} + 5\sqrt{2}$.
Simplify $(\sqrt{7})^2$.
Simplify $\sqrt{20} \div \sqrt{5}$.
Simplify $\sqrt{3} \times \sqrt{5}$.
Simplify $5\sqrt{3} - \sqrt{27}$.
Simplify $\sqrt{10} \times \sqrt{90}$.