Question 178166
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*[tex \Large 5 \times 5 = 25] not 50, so certainly *[tex \Large 5 \neq sqrt(50)]


Similarly, *[tex \Large 4 \times 4 = 16] and *[tex \Large 6 \times 6 = 36], so the rest of your expression is incorrect as well.


You need to use the following rule:


*[tex \Large sqrt{xy} = (sqrt {x} )(sqrt {y})]


Note that


*[tex \Large 50 = 25 \times 2]


*[tex \Large 32 = 16 \times 2]


*[tex \Large 18 = 9 \times 2]


So we can re-write your original expression as:


*[tex \Large 4 sqrt{50} + sqrt{32} - sqrt {18} = 4 sqrt{25}sqrt{2} + sqrt{16}sqrt{2} - sqrt{9}sqrt{2}] 


Since: *[tex \Large sqrt{25} = 5 \text{, }\math sqrt{16} = 4 \text{,and }\math sqrt{9} = 3], we can write:


*[tex \Large  4 * 5 sqrt{2} + 4 sqrt{2} - 3 sqrt{2}] 


Lastly, factor out the *[tex \Large sqrt{2}] to obtain:


*[tex \Large (20 + 4 - 3)sqrt{2} = 21 sqrt {2}]


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