Question

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

the answer was 10√10

Answer 1

Answer: A. 10 sqr 10

Answer 2

`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)`