Question

Simplify each of the following :
(i) 3√4 x 3√16 (ii) 4√1250 / 4√2

Answer 1

Answer:

11 is the correct answer

Answer 2

Given : (i) ³√4 x ³√16

= ³√(4 × 16)

= ³√64

= ³√4³

= (4³)⅓

= 4³×⅓

= 4¹

= 4

Hence, ³√4 x ³√16 = 4

Given : (ii) ⁴√1250 / ⁴√2

= ⁴√(1250/2)

= ⁴√(625 × 2)/2)

= ⁴√625

= ⁴√5⁴

= (5⁴)¼

= 5⁴×¼

= 5¹

= 5

Hence, ⁴√1250 / ⁴√2 = 5

 

Extra information :  

Here we use the law of exponents for real numbers.

Let a (> 0) be a real number  

ⁿ√a × ⁿ√b = ⁿ√ab

ⁿ√a / ⁿ√b = ⁿ√a/ⁿ√b = ⁿ√a/b

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