Question

Help me class8 (surds)​

Answer 1

`\pink{(991 √(2) )/(80) }`

Explanation:

`√(72) - (48)/( √(50) ) - (45)/( √(128) ) + 2 √(98) \\\\`

Simplify the roots.

√72 ⇒ 6√2

√50 ⇒ 5√2

√128 ⇒ 8√2

√98 ⇒ 7√2

`6 √(2) - (48)/(5 √(2) ) - (45)/(8 √(2) ) + 2 * 7 √(2) \\\\`

Now, to rationalize the denominator, multiply the numerator and denominator of the fractions (48 / 5√2) by √2 and (45/8√2) by √2.

`6√(2)-(48*√(2) )/(5√(2)*√(2) ) -(45√(2) )/(8√(2)*√(2) ) +14√(2)\\ \\6√(2)-(48√(2) )/(5*2 ) -(45√(2) )/(8*2 ) +14√(2)\\\\6√(2)-(48√(2) )/(10 ) -(45√(2) )/(16 ) +14√(2)`

Make the denominator the same to solve the fractions.

`(6√( 2)*80)/(1*80) -(48√(2) *8)/(10*8) -(45√(2)*5 )/(16*5) +(14√(2)*80 )/(1*80) \\\\(480√( 2))/(80) -(384√(2) )/(80) -(225√(2) )/(80) +(1120√(2) )/(80)`

`(991√(80) )/(80)`

Answer 2

• 
  `\cfrac{991√(2) }{80}`

Explanation:

For a start simplify each of the roots:

• 
  `√(72) =√(36*2) =6√(2)`
• 
  `√(50) =√(25*2) =5√(2)`
• 
  `√(128) =√(64*2) =8√(2)`
• 
  `√(98) =√(49*2) =7√(2)`

Now simplify the expression in steps:

`√(72)-\cfrac{48}{√(50) } -\cfrac{45}{√(128) } +2√(98) =`

`6√(2)-\cfrac{48}{5√(2) } -\cfrac{45}{8√(2) } +2*7√(2) =`

`6√(2)-\cfrac{48*8+45*5}{5*8√(2) } +14√(2) =`

`20√(2)-\cfrac{609}{40√(2) } =`

`20√(2)-\cfrac{609*√(2) }{40√(2) *√(2) } =`

`20√(2)-\cfrac{609√(2) }{40*2 } =`

`20√(2)-\cfrac{609√(2) }{80 } =`

`√(2) (20-7\cfrac{49}{80} )=`

`√(2) *12\cfrac{31}{80} =`

`\cfrac{991√(2) }{80}`