Question

4.3 simplify
practice it:
\\(\sqrt{1} = 1\\)
\\(\sqrt{4} = 2\\)
\\(\sqrt{9} = 3\\)
\\(\sqrt{16} = 4\\)
\\(\sqrt{25} = 5\\)
\\(\sqrt{36} = 6\\)
\\(\sqrt{49} = 7\\)
\\(\sqrt{64} = 8\\)
\\(\sqrt{81} = 9\\)
\\(\sqrt{100} = 10\\)
1a. \\(\sqrt{54}\\)
\\(\sqrt{54} = \sqrt{6 \cdot 9}\\)
\\(3 \sqrt{6}\\)
1b. \\(\sqrt{180}\\)
\\(\sqrt{180} = \sqrt{9 \cdot 20} = \sqrt{9 \cdot 4 \cdot 5}\\)
\\(3 \cdot 2\sqrt{5}\\)
\\(6\sqrt{5}\\)
exercises
simplify each expression.

1. \\(\sqrt{28}\\)
2. \\(\sqrt{68}\\)
3. \\(\sqrt{60}\\)
4. \\(\sqrt{7}\\)

Explanation:

1. Simplify $\boldsymbol{\sqrt{28}}$

Step1: Factor 28 into 4×7

$\sqrt{28} = \sqrt{4 \cdot 7}$

Step2: Use square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{4\cdot7}=\sqrt{4}\cdot\sqrt{7}$

Step3: Simplify $\sqrt{4}$

Since $\sqrt{4} = 2$, we have $2\sqrt{7}$

Step1: Factor 68 into 4×17

$\sqrt{68}=\sqrt{4\cdot17}$

Step2: Use square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{4\cdot17}=\sqrt{4}\cdot\sqrt{17}$

Step3: Simplify $\sqrt{4}$

Since $\sqrt{4} = 2$, we have $2\sqrt{17}$

Step1: Factor 60 into 4×15

$\sqrt{60}=\sqrt{4\cdot15}$

Step2: Use square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{4\cdot15}=\sqrt{4}\cdot\sqrt{15}$

Step3: Simplify $\sqrt{4}$

Since $\sqrt{4}=2$, we have $2\sqrt{15}$

Answer:

$2\sqrt{7}$

2. Simplify $\boldsymbol{\sqrt{68}}$