Question

a) Express √√√3+ √12 in the form a√3 where a is an integer. √3 b) (i) Express 1 (5) in the form b√3 where b is an integer. 1 (ii) Express (5) 3 in the form 3 C where c is an integer. √√3 √3 ​

Answer 1

Answer & Step-by-step explanation:

a)

√√√3 + √12

= √√(3)^(1/2) + √(4 x 3)

= √√(√3)^2 + √(4 x √3)^2

= √(√3 + 2√3)

= √3(1 + 2)

= 3√3

Therefore, √√√3 + √12 can be expressed in the form of a√3, where a = 3.

b)

(i)

1 + √(3)

To rationalize the denominator, we multiply the numerator and denominator by √3:

= 1 + √(3) * √(3) / √(3)

= 1 + √(9) / √(3)

= 1 + 3√(3) / 3

= (3 + √(3)) / 3

Therefore, 1 + √(3) can be expressed in the form of b√3, where b = (3 + √3) / 3.

(ii)

(5)^(1/3)

To rationalize the denominator, we multiply the numerator and denominator by √(3):

= (5)^(1/3) * √(3) / √(3)

= (5√(3)) / √(27)

= (5√3) / (3√3)

= (5/3)√3

Therefore, (5)^(1/3) can be expressed in the form of c√3, where c = 5/3.