Question

√(√13-p√10)=√8+√5 find p

Answer 1

√13 - x√10 = √8 + √5
First try and reduce the available roots to forms that are similar to eachother
√10 can be written as √5 × √2
√8 can be written as 2√2

Now the equation becomes,

√13 - x√5 √2 = 2√2+√5
Thus,
x√5√2 + √5 = √13 - 2√2

√5 (x√2 + 1) = √13 - 2√2

x√2 + 1 = (√13 - 2√2) ÷ √5

x√2 = ( (√13 - 2√2) ÷ √5 ) - 1

Taking L.C.M,

x√2 = (√13 - 2√2 - √5) ÷ √5

Thus x= ( √13 / ( √2 √5 ) ) - ( 2 / √5 ) - ( 1 / √2 )

x= ( √13 / ( √10 ) ) - ( 2 / √5 ) - ( 1 / √2 )