Thread: Surds...

(√a+√b)²=a+b+2√ab

determine the square root of 17+6√8


I hope you can help,
thanks.

Originally Posted by glenn101

(√a+√b)²=a+b+2√ab

determine the square root of 17+6√8


I hope you can help,
thanks.

A square root of a+b+2√ab is clearly √a+√b.

Note that 17 + 6√8 = 17 + 2√(9)(8) = 17 + 2√72.

Compare with a+b+2√ab.

Therefore solve the following two equations simultaneously:

a + b = 17 ... (1)
ab = 72 ... (2)

I get a = 9 and b = 8 (and obviously the other solution is a = 8 and b = 9) ......

Then a square root of 17+6√8 is √a+√b = ......