Verified answer

I suppose by "?" you mean the variable to be calculated; then:

√2 1/4 = √5/4?

multiply both sides by 4:

√2 = √5?

Divide both sides by √5:

√2/√5 = ?

Finally:

? = √2/√5 = √2/√5 * (√5/√5) = √10/5

Simplifying the fraction 5/3:

5 = 3 + 2

thus:

5/3 = (3 + 2)/3 = 3/3 + 2/3 = 1 + 2/3