Question

Help me class8 (surds)​

Answer 1

Answer:

• $\cfrac{991\sqrt{2} }{80}$

Step-by-step explanation:

For a start simplify each of the roots:

• $\sqrt{72} =\sqrt{36*2} =6\sqrt{2}$
• $\sqrt{50} =\sqrt{25*2} =5\sqrt{2}$
• $\sqrt{128} =\sqrt{64*2} =8\sqrt{2}$
• $\sqrt{98} =\sqrt{49*2} =7\sqrt{2}$

Now simplify the expression in steps:

$\sqrt{72}-\cfrac{48}{\sqrt{50} } -\cfrac{45}{\sqrt{128} } +2\sqrt{98} =$

$6\sqrt{2}-\cfrac{48}{5\sqrt{2} } -\cfrac{45}{8\sqrt{2} } +2*7\sqrt{2} =$

$6\sqrt{2}-\cfrac{48*8+45*5}{5*8\sqrt{2} } +14\sqrt{2} =$

$20\sqrt{2}-\cfrac{609}{40\sqrt{2} } =$

$20\sqrt{2}-\cfrac{609*\sqrt{2} }{40\sqrt{2} *\sqrt{2} } =$

$20\sqrt{2}-\cfrac{609\sqrt{2} }{40*2 } =$

$20\sqrt{2}-\cfrac{609\sqrt{2} }{80 } =$

$\sqrt{2} (20-7\cfrac{49}{80} )=$

$\sqrt{2} *12\cfrac{31}{80} =$

$\cfrac{991\sqrt{2} }{80}$