Question

int math 2
using square roots
simplify.

1. √24
2. √45
3. √216
4. √20
5. √108
6. √80

name itzel ramir
date 11-21-2

Explanation:

1) Simplify $\boldsymbol{\sqrt{24}}$

Step1: Factor the radicand

Factor 24 into a product of a perfect square and another number: $24 = 4\times6$, where 4 is a perfect square.

Step2: Apply square root property

Use the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0,b\geq0$): $\sqrt{24}=\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}$.

Step3: Simplify the perfect square root

Since $\sqrt{4} = 2$, we get $2\sqrt{6}$.

Step1: Factor the radicand

Factor 45 as $9\times5$, with 9 being a perfect square.

Step2: Apply square root property

$\sqrt{45}=\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}$.

Step3: Simplify the perfect square root

As $\sqrt{9}=3$, the result is $3\sqrt{5}$.

Step1: Factor the radicand

Factor 216 into $36\times6$, where 36 is a perfect square.

Step2: Apply square root property

$\sqrt{216}=\sqrt{36\times6}=\sqrt{36}\times\sqrt{6}$.

Step3: Simplify the perfect square root

Since $\sqrt{36}=6$, we have $6\sqrt{6}$.

Answer:

$2\sqrt{6}$

2) Simplify $\boldsymbol{\sqrt{45}}$