229k views
3 votes
√(112) - √(80) / √(20) - √(28) = ?​

User TechyDude
by
7.5k points

1 Answer

5 votes


\large\underline{\sf{Solution-}}

We need to solve,


(√(112)-√(80))/(√(20)-√(28))

We can write the above mentioned expression as,


\sf\longmapsto(√(2*2*2*2*7)-√(2*2*2*5))/(√(2*2*5)-√(2*2*7))

So,


\sf\longmapsto(√(4*4*7)-√(4*4*5))/(√(2^2*5)-√(2^2*7))

So,


\sf\longmapsto(√(4^2*7)-√(4^2*5))/(√(2^2*5)-√(2^2*7))

Hence,


\sf\longmapsto(4√(7)-4√(5))/(2√(5)-2√(7))

Taking common in respective terms,


\sf\longmapsto(4(√(7)-√(5)))/(2(√(5)-√(7)))

On cancelling 4 with 2,


\sf\longmapsto(4\!\!\!/^(\:2)(√(7)-√(5)))/(2\!\!\!/(√(5)-√(7)))


\sf\longmapsto(2(√(7)-√(5)))/((√(5)-√(7)))

Taking (-) common,


\sf\longmapsto(-2(√(5)-√(7)))/((√(5)-√(7)))

So, (√5 - √7) gets cut,

Hence,


\longmapsto\bf(√(112)-√(80))/(√(20)-√(28))=-2

User Dfranca
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories