I ran into a mathematical problem which I guess I can simplify by product-sum factoring, I learned this approach while studying in Kumon, but I am afraid I have forgotten.
This is the expression:
$\sqrt{10 - 2 \sqrt{ 21 } }.$
Notice that $7\cdot 3$ equal to $21$ and $7+3$ equal to $10$, thus we can factor this by the sum-product method.
How can I tackle this problem by using this algorithm?
Thanks in advance!
Hint:
$$10-2\sqrt{21}=(\sqrt7)^2-2\sqrt7\sqrt3+(\sqrt3)^2.$$