Question

Simplify the radical expression.

2√10 . 3√12


A.12√60
B.5√120
C.12√30
D.6√120


Simplify the radical expression.

√14q . 2√4q

A.3√56q
B.4q√14
C.2√56q^2
D.4√14q^2



Simplify the radical expression by rationalizing the denominator.


4/√11

A.11√4
B.4√11
C.4√11/11
D.√121/11

Answer 1

1) D.
`6√(120)`, 2) C.
`2√(56)q^(2)`, 3) C.
`(4√(11))/(11)`

Explanation:

1) We proceed to simplify the expression given in statement:

(i)
`2√(10)\cdot 3√(12)` Given

(ii)
`(3\cdot 2)\cdot (√(10)\cdot √(12))` Commutative and associative properties

(iii)
`(3\cdot 2)\cdot (10^(0.5)\cdot 12^(0.5))` Definition of square root.

(iv)
`6\cdot (10\cdot 12)^(0.5)` Definition of multiplication/
`a^(c)\cdot b^(c) = (a\cdot b)^(c)`

(v)
`6√(120)` Definition of multiplication/Definition of square root/Result

Answer: D

2) We proceed to simplify the expression given in statement:

(i)
`√(14)q \cdot 2√(4)q` Given

(ii)
`2\cdot (√(14)\cdot √(4))\cdot (q\cdot q)` Commutative and associative properties

(iii)
`2\cdot (14^(0.5)\cdot 4^(0.5))\cdot q^(2)` Definition of square root/Definition of power.

(iv)
`2\cdot (14\cdot 4)^(0.5)\cdot q^(2)`
`a^(c)\cdot b^(c) = (a\cdot b)^(c)`

(v)
`2√(56)q^(2)` Definition of multiplication/Definition of square root/Result

Answer: C

3) We proceed to simplify the expression given in statement:

(i)
`(4)/(√(11))` Given

(ii)
`(4)/(√(11))\cdot (√(11))/(√(11))` Modulative property/Existence of multiplicative inverse.

(iii)
`(4√(11))/(√(11)\cdot √(11))`
`(a)/(b)* (c)/(d) = (a\cdot c)/(b\cdot d)`

(iv)
`(4√(11))/(11^(0.5)\cdot 11^(0.5))` Definition of square root.

(v)
`(4√(11))/(11)`
`a^m\cdot a^(n) = a^(m+n)`/Result

Answer: C