Question

square root
a) write in the simplest radical form.

1. $\sqrt{8}$
2. $\sqrt{162}$
3. $\sqrt{45}$
4. $\sqrt{847}$
5. $\sqrt{27}$
6. $\sqrt{224}$
7. $\sqrt{425}$
8. $\sqrt{735}$
9. $\sqrt{243}$

b) 1) which of the following is the simplest radical form of $\sqrt{600}$?
i) $3\sqrt{10}$
ii) $10\sqrt{6}$
iii) $6\sqrt{10}$
iv) $20\sqrt{3}$

1. find the value of $\sqrt{76}$.

Explanation:

Part A (Simplest Radical Form)

1) $\boldsymbol{\sqrt{8}}$

Step1: Factor 8 into perfect square and other

$8 = 4 \times 2$, where $4$ is a perfect square.
$\sqrt{8} = \sqrt{4 \times 2}$

Step2: Use property $\sqrt{ab}=\sqrt{a}\sqrt{b}$

$\sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

Step1: Factor 162

$162 = 81 \times 2$, $81$ is a perfect square.
$\sqrt{162} = \sqrt{81 \times 2}$

Step2: Apply radical property

$\sqrt{81 \times 2} = \sqrt{81} \times \sqrt{2} = 9\sqrt{2}$

Step1: Factor 45

$45 = 9 \times 5$, $9$ is a perfect square.
$\sqrt{45} = \sqrt{9 \times 5}$

Step2: Simplify

$\sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$

Answer:

$2\sqrt{2}$

2) $\boldsymbol{\sqrt{162}}$