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Which choice is equivalent to the expression below? 5√10+√40+√90

the answer was 10√10

User Erskine
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2 Answers

4 votes

Answer: A. 10 sqr 10

User Umer Sufyan
by
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3 votes

Answer:


5√(10)+√(40) +√(90)=10√(10)

Explanation:

We have the following expression:


5√(10)+√(40) +√(90)

Remember the property of root multiplication:


\sqrt[n]{x*y}=\sqrt[n]{x}\sqrt[n]{y}

Therefore:


√(40)=√(4*10)=√(4)*√(10)=2√(10)

Also:


√(90)=√(9*10)=√(9)*√(10)=3√(10)

Then we have that:


5√(10)+√(40) +√(90)=5√(10)+2√(10)+3√(10)

Remember the property of sum of roots:


a√(b)+2a√(b)=3a√(b)

Finally:


5√(10)+√(40) +√(90)=(5+2+3)√(10)


5√(10)+√(40) +√(90)=10√(10)

User Alexander Nenkov
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