Best solutions to - "How do you solve 3+5−2+3?"

Alexander Day

Answered question

2022-02-07

How do you solve

\sqrt{3 + \sqrt{5}} - \sqrt{2 + \sqrt{3}}

Madison Randolph

Beginner2022-02-08Added 20 answers

Step 1

\sqrt{3 + \sqrt{5}} = \sqrt{a} + \sqrt{b}

You square both sides:

3 + \sqrt{5} = a + 2 \sqrt{a b} + b

And you put:

3 = a + b

\sqrt{5} = 2 \sqrt{a b}

that can be squared again giving:

5 = 4 a b

You must now solve this system in a and b (for both square roots in your original expression).
Step 2
You should get:

\sqrt{3 + \sqrt{5}} = \sqrt{\frac{1}{2}} + \sqrt{\frac{5}{2}}

and

\sqrt{2 + \sqrt{3}} = \sqrt{\frac{1}{2}} + \sqrt{\frac{3}{2}}

.
Try substituring in your original expression and eventually rationalize.

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