Question

5. Which number is the square of 5√2-1? A. 23 - 5√2 B. 15√2-2 C. 51 - 10/2 D. 20√2-5 E. 100 + 4√2​

Answer 1

C. 51 -10√2

Explanation:

You want the square of 5√2 -1.

Square

The square of 5√2 -1 can be found using the distributive property.

`(5√(2)-1)^2=(5√(2)-1)(5√(2)-1)\\\\=5√(2)(5√(2)-1) -1(5√(2)-1)\\\\=(5√(2))(5√(2)) -5√(2)-5√(2)+1\\\\=25(√(2))^2-10√(2)+1\\\\=25\cdot2+1-10√(2)=\boxed{51-10√(2)}`