How to Solve the Algebra Equation With Square Root?

Algebra equation with square roots

Solve the algebra equation with square root, when the math equation is √(x + √(x + 11)) + √(x – √(x + 11)) = 4

Solution to the algebra equation with square roots

We have

√(x + √(x + 11)) + √(x – √(x + 11)) = 4

Let, y = √(x + 11) then

√(x + √(x + 11)) + √(x – √(x + 11)) = 4

⇒ √(x + y) + √(x – y) = 4

⇒ √(x + y) = 4 – √(x – y)

Square both sides, then

x + y = 16 – 2 × 4 × √(x – y) + x – y

⇒ 2y – 16 = – 8√(x – y)

⇒ y – 8 = – 4√(x – y)

Square both sides again

y² – 16y + 64 = 16(x – y)

⇒ y² – 16y + 64 = 16x – 16y

⇒ y² + 64 = 16x

We know, y = √(x + 11) then

x + 11 + 64 = 16x

⇒ 15x = 65

⇒ x = 5

so solution to the algebra equation with square root is 5