Question

Express 4√1250 in its simplest form.

Answer 1

Hi ,

i think it is forth root of 1250 or 4√1250

I answer both questions .

1 ) forth root of 1250 = ( 1250 ) ^ 1/4
      
     expressing 1250 into product of prime

                                  = ( 5 × 5 × 5 × 5 × 2 ) ^ 1/4

                                  = ( 5^4 × 2 ) ^ 1/4

                                  = ( 5^4 )^ 1/4 * ( 2 )^ 1/4  [ ∵ ( ab )^m = a^m × b^n ]

                                  = 5 × ( 2 )^1/4                  [ ∵ ( a^m ) ^n =  ^mn ]

2 ) 4 √(1250) = 4 √ [(5 × 5 ) × ( 5 × 5 ) × 2 ]

                      = 4 × 5 × 5 × √2

                      = 100√2

I hope this helps you .

Answer 2

100√2 is the answer of this question