Question

value of fourth root 124+32√15​

Answer 1

Given: The expression 124+32√15​

To find: The value of fourth root 124+32√15​ .

Solution:

• Now we have given the term as:

            124 + 32√15​

• We can write it as:

            64 + 60 + 32√15​

            (8)^2 + (2√15)^2 + 2x8x2√15

• Now this in the form (a^2 + b^2 + 2ab) = (a+b)^2

            (8 + 2√15)^2

• We can write it as:

            ((√3)^2 + (√5)^2 + 2√3√5)^2

• Now this in the form (a^2 + b^2 + 2ab) = (a+b)^2

            ( (√3 + √5)^2 )^2

            (√3 + √5)^4

• Now :

            fourth root 124+32√15​  = (√3 + √5)^4

            124+32√15​  = ((√3 + √5)^4 )^1/4

• Cancelling the power we get:

            (√3 + √5)

Answer:

             So the value of fourth root 124+32√15​  is (√3 + √5).