Question

what do you get when you cross an owl and an oyster?
simplify the radicals. find each answer at the right. write the letter of the item in the box or boxes next to the answer.
$\boldsymbol{\text{o: }\sqrt{18} = }$
$\boldsymbol{\text{e: }\sqrt{48} = }$
$\boldsymbol{\text{i: }\sqrt{80} = }$
$\boldsymbol{\text{p: }\sqrt{245} = }$
$\boldsymbol{\text{w: }\sqrt{162} = }$
$\boldsymbol{\text{o: }\sqrt{196} = }$
$\boldsymbol{\text{d: }\sqrt{\frac{1}{2}} = }$
$\boldsymbol{\text{a: }\frac{\sqrt{300}}{\sqrt{5}} = }$
$\boldsymbol{\text{l: }\frac{\sqrt{56}}{\sqrt{7}} = }$
$\boldsymbol{\text{r: }\frac{\sqrt{21}}{\sqrt{7}} = }$
$\boldsymbol{\text{f: }\frac{\sqrt{45}}{3} = }$
$\boldsymbol{\text{m: }\frac{\sqrt{24}}{\sqrt{20}} = }$

	$\boldsymbol{7\sqrt{5}}$	$\boldsymbol{4\sqrt{3}}$	$\boldsymbol{2\sqrt{15}}$	$\boldsymbol{\sqrt{3}}$	$\boldsymbol{2\sqrt{2}}$	$\boldsymbol{3\sqrt{2}}$	$\boldsymbol{14}$	$\boldsymbol{\sqrt{5}}$	$\boldsymbol{9\sqrt{2}}$	$\boldsymbol{4\sqrt{5}}$	$\boldsymbol{3\sqrt{2}}$	$\boldsymbol{\frac{1}{2}\sqrt{2}}$	$\boldsymbol{14}$	$\boldsymbol{\frac{1}{5}\sqrt{30}}$

objective: to simplify expressions involving square root
78
geometry: plane & simple
© 1989 creative publications

Explanation:

Step1: Simplify $\sqrt{80}$

Factor 80 into $16 \times 5$, so $\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$

Step2: Simplify $\sqrt{245}$

Factor 245 into $49 \times 5$, so $\sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} = 7\sqrt{5}$

Step3: Simplify $\sqrt{196}$

$\sqrt{196}$ is the square root of 14 squared, so $\sqrt{196} = 14$

Step4: Simplify $\frac{\sqrt{300}}{\sqrt{5}}$

Use quotient rule: $\frac{\sqrt{300}}{\sqrt{5}} = \sqrt{\frac{300}{5}} = \sqrt{60} = \sqrt{4 \times 15} = 2\sqrt{15}$

Step5: Simplify $\sqrt{\frac{1}{2}}$

Rationalize denominator: $\sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{2}}{2} = \frac{1}{2}\sqrt{2}$

Step6: Simplify $\frac{\sqrt{56}}{\sqrt{7}}$

Use quotient rule: $\frac{\sqrt{56}}{\sqrt{7}} = \sqrt{\frac{56}{7}} = \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$

Step7: Simplify $\frac{\sqrt{45}}{3}$

Factor 45: $\frac{\sqrt{9 \times 5}}{3} = \frac{3\sqrt{5}}{3} = \sqrt{5}$

Step8: Simplify $\frac{\sqrt{24}}{\sqrt{20}}$

Use quotient rule: $\frac{\sqrt{24}}{\sqrt{20}} = \sqrt{\frac{24}{20}} = \sqrt{\frac{6}{5}} = \frac{\sqrt{6} \times \sqrt{5}}{\sqrt{5} \times \sqrt{5}} = \frac{\sqrt{30}}{5} = \frac{1}{5}\sqrt{30}$

Step9: Simplify $\frac{\sqrt{21}}{\sqrt{7}}$

Use quotient rule: $\frac{\sqrt{21}}{\sqrt{7}} = \sqrt{\frac{21}{7}} = \sqrt{3}$

Answer:

• $\boldsymbol{\sqrt{80} = 4\sqrt{5}}$ (matches box with $\boldsymbol{4\sqrt{5}}$)
• $\boldsymbol{\sqrt{245} = 7\sqrt{5}}$ (matches box with $\boldsymbol{7\sqrt{5}}$)
• $\boldsymbol{\sqrt{196} = 14}$ (matches box with $\boldsymbol{14}$)
• $\boldsymbol{\frac{\sqrt{300}}{\sqrt{5}} = 2\sqrt{15}}$ (matches box with $\boldsymbol{2\sqrt{15}}$)
• $\boldsymbol{\sqrt{\frac{1}{2}} = \frac{1}{2}\sqrt{2}}$ (matches box with $\boldsymbol{\frac{1}{2}\sqrt{2}}$)
• $\boldsymbol{\frac{\sqrt{56}}{\sqrt{7}} = 2\sqrt{2}}$ (matches box with $\boldsymbol{2\sqrt{2}}$)
• $\boldsymbol{\frac{\sqrt{45}}{3} = \sqrt{5}}$ (matches box with $\boldsymbol{\sqrt{5}}$)
• $\boldsymbol{\frac{\sqrt{24}}{\sqrt{20}} = \frac{1}{5}\sqrt{30}}$ (matches box with $\boldsymbol{\frac{1}{5}\sqrt{30}}$)
• $\boldsymbol{\frac{\sqrt{21}}{\sqrt{7}} = \sqrt{3}}$ (matches box with $\boldsymbol{\sqrt{3}}$)

Matching letters to answers (to solve the riddle):

• $7\sqrt{5}$ ↔ $\boldsymbol{P}$
• $4\sqrt{3}$ ↔ $\boldsymbol{E}$
• $2\sqrt{15}$ ↔ $\boldsymbol{A}$
• $\sqrt{3}$ ↔ $\boldsymbol{R}$
• $3\sqrt{2}$ ↔ $\boldsymbol{S}$, $\boldsymbol{G}$
• $2\sqrt{2}$ ↔ $\boldsymbol{L}$
• $9\sqrt{2}$ ↔ $\boldsymbol{W}$
• $\sqrt{5}$ ↔ $\boldsymbol{F}$
• $14$ ↔ $\boldsymbol{O}$
• $\frac{1}{2}\sqrt{2}$ ↔ $\boldsymbol{D}$
• $\frac{1}{5}\sqrt{30}$ ↔ $\boldsymbol{M}$

The solved riddle (arranging letters by answer boxes) spells: A S M A R T O W L