Question

non-perfect square roots: use the perfect square numbers below to break the problem apart:
perfect squares:
□□,□,□,□,□,□,□,□,□,□ etc....
put the following in simplest radical form:

1. √24

2√6

1. √48

4√3

1. √72

6√2

1. √63

1. √90

3√10

1. √175

5√7

1. √162

1. √245

1. √343

1. √117

1. √28

1. √450

non-perfect cube roots: use the perfect cube numbers below to break the problem apart:
perfect cubes:
□,□,□,□,□,□,□,□ etc....

Explanation:

Problem 4: $\boldsymbol{\sqrt{63}}$

Step1: Factor 63 into perfect square and other

Factor 63: $63 = 9\times7$, where 9 is a perfect square.
$\sqrt{63}=\sqrt{9\times7}$

Step2: Use square root property

Use $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a\geq0,b\geq0$):
$\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}$

Step3: Simplify $\sqrt{9}$

$\sqrt{9} = 3$, so:
$3\times\sqrt{7}=3\sqrt{7}$

Problem 7: $\boldsymbol{\sqrt{162}}$

Step1: Factor 162 into perfect square and other

Factor 162: $162 = 81\times2$, 81 is a perfect square.
$\sqrt{162}=\sqrt{81\times2}$

Step2: Use square root property

$\sqrt{81\times2}=\sqrt{81}\times\sqrt{2}$

Step3: Simplify $\sqrt{81}$

$\sqrt{81} = 9$, so:
$9\times\sqrt{2}=9\sqrt{2}$

Problem 8: $\boldsymbol{\sqrt{245}}$

Step1: Factor 245 into perfect square and other

Factor 245: $245 = 49\times5$, 49 is a perfect square.
$\sqrt{245}=\sqrt{49\times5}$

Step2: Use square root property

$\sqrt{49\times5}=\sqrt{49}\times\sqrt{5}$

Step3: Simplify $\sqrt{49}$

$\sqrt{49} = 7$, so:
$7\times\sqrt{5}=7\sqrt{5}$

Problem 9: $\boldsymbol{\sqrt{343}}$

Answer:

Step1: Factor 450 into perfect square and other

Factor 450: $450 = 225\times2$, 225 is a perfect square.
$\sqrt{450}=\sqrt{225\times2}$

Step2: Use square root property

$\sqrt{225\times2}=\sqrt{225}\times\sqrt{2}$

Step3: Simplify $\sqrt{225}$

$\sqrt{225} = 15$, so:
$15\times\sqrt{2}=15\sqrt{2}$

Final Answers:

1. $3\sqrt{7}$
2. $9\sqrt{2}$
3. $7\sqrt{5}$
4. $7\sqrt{7}$
5. $3\sqrt{13}$
6. $2\sqrt{7}$
7. $15\sqrt{2}$