Need help with triangles to find out if it is right, acute or obtuse.

Question

14,√61,√257

2√2,√5,√13

Answer 1

To be right-angled, the sum of the squares of the two smaller numbers must equal the square of the largest.
so , is 14^2 + (√61)^2 = √257^2
or, is
196 + 61 = 257 ?? If true, they will form a right-angled triangle.

Decide your second one in the same way.

Answer 2

For this one 2√2,√5,√13 I have this answer as:
2√2^2+√5^2=√13^2
=4+5=13
=9<13 obtruse triangle, is this correct

Answer 3

(2√2)^2 = ?

Answer 4

It's 4

Answer 5

Would this be a right triangle
2√2,√5,√13

Answer 6

For this one 2√2,√5,√13 I have this answer as:
2√2^2+√5^2=√13^2
=4+5=13
=9<13 obtruse or right triangle, is this formula correct

Answer 7

(2√2)^2 = 2*2 * (√2)^2 = 4*2 = 8
or,
2√2 = √4*√2 = √8

√8^2 + √5^2 = 13
so, a right triangle