Answer:
see attached
Step-by-step explanation:
The Pythagorean theorem can be used to find the hypotenuse associated with each pair of legs. That tells you ...
c² = a² +b² . . . . . legs a, b; hypotenuse c
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alternate form of Pythagorean theorem
For the purpose of this problem, it is convenient to consider a slightly different form of the equation.
For legs √a and √b, the hypotenuse √c is given by ...
(√c)² = (√a)² +(√b)²
c = a +b
That is ...
legs √a, √b ⇒ hypotenuse √(a+b)
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application to this problem
Since the legs are (mostly) given in terms of square roots, the value under the radical for the hypotenuse is simply the sum of those:
legs: √1, √2 ⇒ hypotenuse √(1+2) = √3
legs: √2, √3 ⇒ hypotenuse √(2+3) = √5
legs: √5, √3 ⇒ hypotenuse √(5+3) = √8
legs: √5, √1 ⇒ hypotenuse √(5+1) = √6
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Additional comment
You may not see the leg lengths given as square roots very often. This is a rather unusual set of problems for hypotenuse length.
