SIMPLIFYING VARIABLE EXPRESSIONS WITH SQUARE ROOTS

Simplify each radical expression. Use absolute value symbols when needed.

Problem 1 :

√16x²

Solution :

√16x² = √ (4∙4∙x∙x)

√16x² = 4x

Problem 2 :

√0.25x⁶

Solution :

√0.25x⁶ = √ (0.5) (0.5).x^3.x³

√0.25x⁶ = 0.5x³

Problem 3 :

√x⁸y¹⁸

Solution :

√x⁸y¹⁸ = √ (x⁴∙x⁴∙y⁹∙y⁹)

√x⁸y¹⁸ = x⁴∙x⁹

Problem 4:

√64b⁴⁸

Solution :

√64b⁴⁸ = √ (8∙8∙b²⁴∙b²⁴)

√64b⁴⁸ = 8b²⁴

Problem 5 :

-√64a³

Solution :

-√64a³ = (4∙4∙4∙a∙a∙a)

-√64a³ = - 4a

Problem 6 :

√27y⁶

Solution :

√27y⁶ = (3∙3∙3∙y²∙y²∙y²)

√27y⁶ = 3y²

Problem 7 :

√x⁸y¹²

Solution :

√x⁸y¹² = (x²∙x²∙x²∙x²∙y³∙y³∙y³∙y³)

√x⁸y¹² = x²y³

Problem 8 :

√x¹⁰

Solution :

√x^{10 =} √x⁵ x⁵

= x⁵

Problem 9 :

√y²

Solution :

√y² = √(y∙y)

√y² = y

Problem 10 :

√b²

Solution :

√b² = √ (b∙b)

√b² = b

Problem 11 :

√49x²

Solution :

√49x² = √ (7∙7∙x∙x)

√49x² = 7x

Problem 12 :

√100y²

Solution :

√100y² = √ (10∙10∙y∙y)

√100y² = 10y

Problem 13 :

-√64a²

Solution :

-√64a² = -√ (8∙8∙a∙a)

-√64a² = - 8a 

Problem 14 :

-√25x²

Solution :

-√25x² = -√(5∙5∙x∙x)

-√25x² = - 5x

Problem 15 :

√144x²y²

Solution :

√144x²y² = √(12∙12∙x∙x∙y∙y)

√144x²y² = 12xy

Problem 16 :

√196a²b²

Solution :

√196a²b² = √ (14∙14∙a∙a∙b∙b)

√196a²b² = 14ab