Question

If\[\displaystyle\frac{\sqrt{600} + \sqrt{150} + 4\sqrt{54}}{6\sqrt{32} - 3\sqrt{50} - \sqrt{72}} = a\sqrt{b},\]where $a$ and $b$ are integers and $b$ is as small as possible, find $a+b.$

Answer 1

12

Explanation:

Answer 2

9514 1404 393

Answer:

12

Explanation:

Apparently, you want the sum a+b when ...

`\[\displaystyle(√(600) + √(150) + 4√(54))/(6√(32) - 3√(50) - √(72)) = a√(b),\]`

A calculator can show you the expression on the left evaluates to √243. In simplest terms, that is 9√3, so we have a=9, b=3 and ...

a+b = 9+3 = 12