Question

11. Write each of the following in the form a√b where a and b are integers and b is as small as possible. A rational number is an integer or fraction.​

Answer 1

`(√(2) *3)/8`
`(√(2) *3)/8`Answer:

Explanation:

a)
`√(72) /64`

`( √(2) * 6)/64` 72 is = 2*36, which in turn is =6*
`√(2)`

`√(2)*( 6/64)` Isolate the (6/64) and then reduce to (3/32)

`√(2)*( 3/32)`

b)
`√(75) /16`

`√(75)= √(3*25)`

`√(3*25) = √(3) *5`

`(√(3) *5)/16`

`√(3)*( 5/16)`

c)
`√(18) /8`

`√(18) = √(2) *√(9)`

`(√(2) *√(9))/8`

`(√(2) *3)/8`

(3/8)*
`√(2)`

d)
`√(32))/144`

`√(32) = √(2) *√(16)`

`√(32) = √(2) *4`

`(√(32)/144\=√(2) *4)/144`

`(√(32) = √(2)*√(16)`

`(√(32) = √(2)*4`

`√(32))/144 = (√(2)*4)/144`

`√(2) *(4/144)`

`= (1/36)*√(2)`

Answer 2

see explanation

Explanation:

using the rule of radicals

`√(ab)` =
`√(a)` ×
`√(b)`

(a)

`(√(72) )/(64)` =
`(√(36(2)) )/(64)` =
`(√(36)(√(2)) )/(64)` =
`(6√(2) )/(64)` =
`(3)/(32)`
`√(2)`

(b)

`(√(75) )/(16)` =
`(√(25(3)) )/(16)` =
`(√(25(3)) )/(16)` =
`(√(25)(√(3)) )/(16)` =
`(5√(3) )/(16)` =
`(5)/(16)`
`√(3)`

(c)

`(√(18) )/(8)` =
`(√(9(2)) )/(8)` =
`(√(9)(√(2)) )/(8)` =
`(3√(2) )/(8)` =
`(3)/(8)`
`√(2)`

(d)

`(√(32) )/(144)` =
`(√(16(2)) )/(144)` =
`(√(16)(√(2)) )/(144)` =
`(4√(2) )/(144)` =
`(1)/(36)`
`√(2)`