Surds Worked Solutions — GCSE Maths

Find the largest square factor of 8

Look for the biggest perfect square dividing 8; here $4 = 2^2$.

Split the surd

Use $\sqrt{ab} = \sqrt{a}\times\sqrt{b}$ to separate the square part.

Root the square part

$\sqrt{4}$ is exactly 2.

Write the simplified surd

So $\sqrt{8} = 2\sqrt{2}$.

Find the largest square factor of 12

Look for the biggest perfect square dividing 12; here $4 = 2^2$.

Split the surd

Use $\sqrt{ab} = \sqrt{a}\times\sqrt{b}$ to separate the square part.

Root the square part

$\sqrt{4}$ is exactly 2.

Write the simplified surd

So $\sqrt{12} = 2\sqrt{3}$.

Find the largest square factor of 18

Look for the biggest perfect square dividing 18; here $9 = 3^2$.

Split the surd

Use $\sqrt{ab} = \sqrt{a}\times\sqrt{b}$ to separate the square part.

Root the square part

$\sqrt{9}$ is exactly 3.

Write the simplified surd

So $\sqrt{18} = 3\sqrt{2}$.

Find the largest square factor of 20

Look for the biggest perfect square dividing 20; here $4 = 2^2$.

Split the surd

Use $\sqrt{ab} = \sqrt{a}\times\sqrt{b}$ to separate the square part.

Root the square part

$\sqrt{4}$ is exactly 2.

Write the simplified surd

So $\sqrt{20} = 2\sqrt{5}$.

Find the largest square factor of 50

Look for the biggest perfect square dividing 50; here $25 = 5^2$.

Split the surd

Use $\sqrt{ab} = \sqrt{a}\times\sqrt{b}$ to separate the square part.

Root the square part

$\sqrt{25}$ is exactly 5.

Write the simplified surd

So $\sqrt{50} = 5\sqrt{2}$.