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What is 2sqrt(147) + 2sqrt(27) - sqrt(98)

Davis  Mar 2, 2017

Best Answer 

 #1
avatar+92805 
+10

Hi Davis,

look, study, learn :))

 

2sqrt(147) + 2sqrt(27) - sqrt(98)

 

 

To simplify a square root you must look for a square number that goes into it

square numbers are

\(1^1=1 \qquad \text{not helpful though}\\ 2^2=4\\3^2=9\\4^2=16\\etc\\\)

 

I can see tht

147 = 49*3

27=9*3

98=49*2

 

so I have

\(2\sqrt{147} + 2\sqrt{27} - \sqrt{98}\\ =2*\sqrt{49*3} \quad+\quad 2*\sqrt{9*3} \quad-\quad \sqrt{49*2}\\ =2*\sqrt{49}*\sqrt3 \quad+\quad 2*\sqrt9*\sqrt3 \quad-\quad \sqrt{49}*\sqrt2\\ =2*7*\sqrt3 \quad+\quad 2*3*\sqrt3 \quad-\quad7*\sqrt2\\ =14\sqrt3 \quad+\quad 6\sqrt3 \quad-\quad7\sqrt2\\ =20\sqrt3 \quad -\quad7\sqrt2\\\)

After you look and study, ask any questions that you want to :)

Melody  Mar 2, 2017
 #1
avatar+92805 
+10
Best Answer

Hi Davis,

look, study, learn :))

 

2sqrt(147) + 2sqrt(27) - sqrt(98)

 

 

To simplify a square root you must look for a square number that goes into it

square numbers are

\(1^1=1 \qquad \text{not helpful though}\\ 2^2=4\\3^2=9\\4^2=16\\etc\\\)

 

I can see tht

147 = 49*3

27=9*3

98=49*2

 

so I have

\(2\sqrt{147} + 2\sqrt{27} - \sqrt{98}\\ =2*\sqrt{49*3} \quad+\quad 2*\sqrt{9*3} \quad-\quad \sqrt{49*2}\\ =2*\sqrt{49}*\sqrt3 \quad+\quad 2*\sqrt9*\sqrt3 \quad-\quad \sqrt{49}*\sqrt2\\ =2*7*\sqrt3 \quad+\quad 2*3*\sqrt3 \quad-\quad7*\sqrt2\\ =14\sqrt3 \quad+\quad 6\sqrt3 \quad-\quad7\sqrt2\\ =20\sqrt3 \quad -\quad7\sqrt2\\\)

After you look and study, ask any questions that you want to :)

Melody  Mar 2, 2017

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