Math question on surds- please help with explanation

  • 0 votes

It asks you to simplify:

√1/2+ √1/4+ √1/8

the answer is:

1/2+ 3/4√2

please perform it in steps so I understand, Thank you

Posted Sat 22nd December, 2012 @ 06:03 by Cymbeline

1 Answer

  • 1 vote

√1/2 + √1/4 + √1/8

= 1/√2 + 1/2 + 1/√8 (As √(x/y) is equals to √x/√y)

= 1/√2 + 1/√8 + 1/2 (Rearranging the terms)

= (√8 + √2) / (√8 x √2) + 1/2 (Adding 1/√2 to 1/√8 by making their denominators identical)

= (2√2 + √2) / 4 + 1/2 (As √8 = √(2x4) = 2√2)

= (3√2 / 4) + 1/2 (As 2√2 + √2 = 3√2)

= 1/2 + 3/4√2 (As (3√2 / 4) is the same as 3/4√2, followed by rearranging the terms)

Answered Sat 22nd December, 2012 @ 11:01 by Rosa
Edited by Rosa on Sat 22nd December, 2012 @ 15:32