Simplify by factoring -√45?

1) - (sq rt 45) = - 1(sq rt 9)(sq rt 5). Sq rt 9 = 3, so the Answer is - 3(sq rt 5).

2) (sq rt 180) = (sq rt 36)(sq rt 5) = 6(sq rt 5) Answer

3) (sq rt 8x^2y) = (sq rt 4x^2)(sq rt 2y) = 2x(sq rt 2y). Answer

-√45 = -√(9 * 5) = -1 * √9 * √5 = -1 * 3 * √5 = -3√5

√180 = √(36 * 5) = √36 * √5 = 6 * √5 = 6√5

√(8x^2y) = √8 * √(x^2) * √y = √(4 * 2) * x * √y = √4 * √2 * x * √y = 2 * √2 * x * √y = 2x * √(2 * y) = 2x√(2y)

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Remember these rules when you're working with exponents.

xº = 1
x¹ = x
x^(-a) = 1 / xª
xª * x^b = x^(a + b)
xª / x^b = x^(a - b)
(xª)^b = x^(a * b)
(xy)ª = (x * y)ª = xª * yª
√a = a^(½)
ª√x = x^(1 / a)
(x / y)ª = xª / yª
√(x * y) = √x * √y
ª√(x * y) = ª√x * ª√y

Simplifying By Factoring

- √ 45 = - 3 √5

√ 180 = √ ( 36 x 5 ) = 6 √ 5

√ [ 8 x ² y ] = 2 √ 2 ( x ) √ y = ( 2 x ) √ ( 2y )

1)
-√45
= -√(3^2 * 5)
= -√(3^2) * √5
= -3 * √5
= -3√5

2)
√180
= √(3^2 * 2^2 * 5)
= 3 * 2 * √5
= 6√5

3)
√(8x^2y)
= √(2^2 * x^2 * 2 * y)
= 2x√(2y)

1) squareroot of 45 = squareroot (9 x 5)
9 has a squareroot, so you can take that out from under the squareroot sign
and you get -3(squareroot 5)
2) same thing squareroot 180 = squareroot( 36 x 5) 36 has a squareroot, so you get
6(squareroot 5)

3) squareroot 8x^2y = squareroot (4 times 2 times x^2y) 4 and x^2 have squareroots, so you get
2x(squareroot 2y)

sqrt (45) = sqrt(9)*sqrt(5)= 3*sqrt(5)


sqrt(180) = sqrt(9*4*5) = sqrt(9)*sqrt(4)*sqrt(5)= 3*2*sqrt(5)= 6*sqrt(5)


sqrt(8)*sqrt(x^2)*sqrt(y)= 2*sqrt(2)*x*sqrt(y)