S3 Homework - Surds and Indices

[YouAreTheWeakestLinkGoodbye1]

I really need help trying to assist ds with this homework sheet. We solved question 1 but are completely stuck with how to solve the other 4. There are no examples in his jotter or the textbook and we can't find anything helpful online? Help with any one of the questions would be appreciated!

For number 2, use Pythagoras. a2 + b2 = c^2.
So (root32)2 + b2 = (root50)^2.
32 + b^2 = 50
b^2 = 18
b = root 18 = 3 root 2 (if they have to simplify, though given the lengths in the problem, it doesn’t look like they do!).

1. m^3 x root m

= m3 x m1/2 (because roots are fractional powers) = m^7/2 (add the two powers; 3 + 1/2 = 7/2)

1. a1/2 (a1/2 -2)

• a1 - 2a1/2 (multiply out brackets; add powers if base is the same).

= a - 2a^1/2 (or a - 2a x root a

= 4/ root 7
= 4xroot 7/ (root 7 x root 7 ) [multiplying top and bottom by root7, because root7/root7 = 1 so you can multiply by it without changing anything]
= 4 x root7/ 7 [ because root 7 x root 7 equals 7]

Sorry if formatting goes wrong. Also some of the numbers are quite small, so I hope i’ve read it right!

typo at the end of number 4, the simplified bit in brackets should read:
a - 2root a
not
a - 2a root a

It would have been easier with a root sign!

Crotchet - good job, all looks correct to me (I can't read the questions, so assuming you've copied them correctly).

Only comment to add is that "rational" means no square roots (or cube roots etc), so the denominator (the bottom number in the fraction) needs to be cleared of the root 7, and Crotchet's shown exactly how to do this.