# Thread: Basic Arithmetic and Surds

1. ## Basic Arithmetic and Surds

Express (2root5 - 3root10)^2 in the form a+broot2 and hence find the values of a and b. If you can please help and explain the method and how to solve equations similar to this. Thanks

2. ## Re: Basic Arithmetic and Surds

That is not an equation. Anyway:

$(a-b)^2=a^2-2ab+b^2$, so:

$(2\sqrt 5-3\sqrt {10})^2=(2\sqrt 5)^2-2\cdot 2\sqrt 5 \cdot 3\sqrt {10} + (3\sqrt {10})^2=$

$=4\cdot 5-12\sqrt{5\cdot 10}+3\cdot 10=20-12\cdot 5 \sqrt 2 +30=50-60\sqrt 2$

a = 50, b = -60

3. ## Re: Basic Arithmetic and Surds

Alice

show us some of your work...apply the well known identity (a-b)^2 =a^2+b^2-2ab....where a and b could be anything...in your case 2root5 or 2root10......try it