SIMPLIFYING SQUARE ROOTS WITH VARIABLES WORKSHEET

Problem 1 : 

Simplify the following expression :

√(64x²) + √(196x²)

Problem 2 : 

Simplify the following expression :

√(4x⁴) - √(16x⁴)

Problem 3 : 

Simplify the following expression :

√(100x²y⁴) + √(121x²y⁴)

Problem 4 : 

Simplify the following expression :

√(36x⁴y²)√(25x²y⁴)

Problem 5 : 

Simplify the following expression :

√(36x²y⁴z⁶) / √(4x⁶y⁴z²)

Detailed Answer Key

Problem 1 : 

Simplify the following expression :

√(64x²) + √(196x²)

Solution : 

√(64x²)  =  √(8 ⋅ 8 ⋅ x ⋅ x)  =  8x

√(196x²)  =  √(14 ⋅ 14 ⋅ x ⋅ x)  =  14x

Then,

√(64x²) + √(196x²)  =  8x + 14x

√(64x²) + √(196x²)  =  22x

Problem 2 : 

Simplify the following expression :

√(4x⁴) - √(16x⁴)

Solution : 

√(4x⁴)  =  √(2 ⋅ 2 ⋅ x² ⋅ x²)  =  2x²

√(16x⁴)  =  √(4 ⋅ 4 ⋅ x² ⋅ x²)  =  4x²

Then, 

√(4x⁴) - √(16x⁴)  =  2x² - 4x²

√(4x⁴) - √(16x⁴)  =  -2x²

Problem 3 : 

Simplify the following expression :

√(100x²y⁴) + √(121x²y⁴)

Solution : 

√(100x²y⁴)  =  √(10 ⋅ 10 ⋅ x ⋅ x ⋅ y² ⋅ y²)  =  10xy²

√(121x²y⁴)  =  √(11 ⋅ 11 ⋅ x ⋅ x ⋅ y² ⋅ y²)  =  11xy²

Then, 

√(100x²y⁴) + √(121x²y⁴)  =  10xy² + 11xy²

√(100x²y⁴) + √(121x²y⁴)  =  21xy²

Problem 4 : 

Simplify the following expression :

√(36x⁴y²)√(25x²y⁴)

Solution : 

√(36x⁴y²)  =  √(6 ⋅ 6 ⋅ x² ⋅ x² ⋅ y ⋅ y)  =  6x²y

√(25x²y⁴)  =  √(5 ⋅ 5 ⋅ x ⋅ x ⋅ y² ⋅ y²)  =  5xy²

Then, 

√(36x⁴y²)√(25x²y⁴)  =  (6x²y)(5xy²)

√(36x⁴y²)√(25x²y⁴)  =  30x³y³

Problem 5 : 

Simplify the following expression :

√(36x²y⁴z⁶) / √(4x⁶y⁴z²)

Solution : 

√(36x²y⁴z⁶)  =  √(6 ⋅ 6 ⋅ x ⋅ x ⋅ y² ⋅ y² ⋅ z³ ⋅ z³)  =  6xy²z³

√(4x⁶y⁴z²)  =  √(2 ⋅ 2 ⋅ x³ ⋅ x³ ⋅ y² ⋅ y² ⋅ z ⋅ z)  =  2x³y²z

Then, 

√(36x²y⁴z⁶) / √(4x⁶y⁴z²)  =  (6xy²z³) / (2x³y²z)

√(36x²y⁴z⁶) / √(4x⁶y⁴z²)  =  2x^1-3y^2-2z^3-1

√(36x²y⁴z⁶) / √(4x⁶y⁴z²)  =  2x^-2y⁰z²

√(36x²y⁴z⁶) / √(4x⁶y⁴z²)  =  2z²/x²

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