Represent x3 + 3x2 + 3x + 1 in quadratic surd.1. \(\sqrt {{{\left( {x

1.	Represent x3 + 3x2 + 3x + 1 in quadratic surd.1. \(\sqrt {{{\left( {x + 1} \right)}^3}} \)2. \({\left( {x + 1} \right)^{\frac{3}{2}}}\)3. \({\left( {x + 1} \right)^{\frac{2}{3}}}\)4. \(\sqrt {{{\left( {x + 1} \right)}^6}} \)
Answer» Correct Answer - Option 4 : \(\sqrt {{{\left( {x + 1} \right)}^6}} \) Given: Expression: x³ + 3x² + 3x + 1 Concept used: Quadratic surd: An expression that contains a square root under which is a rational number which is not a perfect square. Calculation: x³ + 3x² + 3x + 1 = (x + 1)³ The expression (x + 1)³itself is not a perfect square. Then, to represent it in quadratic surd form, we just need to write it in the form of a perfect square under the square root. (x + 1)³ = √(x + 1)⁶ ∴ The quadratic surd form of the above expression is √(x + 1)⁶.

Represent x3 + 3x2 + 3x + 1 in quadratic surd.1. \(\sqrt {{{\left( {x + 1} \right)}^3}} \)2. \({\left( {x + 1} \right)^{\frac{3}{2}}}\)3. \({\left( {x + 1} \right)^{\frac{2}{3}}}\)4. \(\sqrt {{{\left( {x + 1} \right)}^6}} \)

Answer» Correct Answer - Option 4 : \(\sqrt {{{\left( {x + 1} \right)}^6}} \)

Given:

Expression: x³ + 3x² + 3x + 1

Concept used:

Quadratic surd: An expression that contains a square root under which is a rational number which is not a perfect square.

Calculation:

x³ + 3x² + 3x + 1 = (x + 1)³

The expression (x + 1)³itself is not a perfect square.

Then, to represent it in quadratic surd form, we just need to write it in the form of a perfect square under the square root.

(x + 1)³ = √(x + 1)⁶

∴ The quadratic surd form of the above expression is √(x + 1)⁶.