express in simplified form

Question

_{^{√448x∧8y∧19}}

Answer 1

Hi, Mondrea.

 

to simplify a radical, we break it up into perfect squares. For variables, even exponents are perfect squares.

 

448 = 64 * 7

x⁸ is a square

y¹⁹ = y¹⁸ * y

 

So, we have √64 * √7 * √x⁸ * √y¹⁸ * √y

= 8 * √7 * x⁴ * y⁹ * √y

= 8x⁴y⁹√7y

 

Hope that helps!

Kathye P.

 

BTW, on large numbers, you can also break them down a little at a time, if that helps.

For example, 448 = 4 * 4 * 4 * 7

 

Answer 2

Simplify √(448 x^8 y^19)

 

Find perfect square factors:

 

448 = 4*112 = 4*4*28 = 4*4*4*7

= (4^2)*(2^2)*7 = (8^2)*7

 

x^8 = (x^4)^2

 

y^19 = y*(y^18) = y*(y^9)^2

 

√(448 x^8 y^19)

 

= √( (8^2)*7*(x^4)^2*y*(y^9)^2 )

 

= √( (8^2)*(x^4)^2*(y^9)^2*7*y )

 

= 8*(x^4)*(|y|^9)*√(7 y)

 

The absolute value on y^9 is because √((y^9)^2) is always positive so it's simplified version must be positive too.