Question

Write in surd form" {13}^{\frac{5}{2} } " alt=" {13}^{\frac{5}{2} } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

sqrt(13^2)

Step-by-step explanation:

this is the radical form of 13^(5/2)

Answer 2

Answer:   169 √(13)

Step-by-step explanation:

We can rewrite $13^{\frac{5}{2} }$ in a form that makes it easier to see:

13^{\frac{5}{2} }  =  √[(13)⁵]

Now, we want to factorise and rewrite (13)⁵ so that one of the factors is a perfect square

       13⁵  = 13⁴ × 13     (where 13⁴ is a perfect square)

⇒  √[(13)⁵]  = √[ 13⁴ × 13]                     [separate each term on LHS]

                  =  √(13⁴)   ×    √(13)           [square root the perfect square]

                  =   13² √(13)                     [simplify]

                  =   169 √(13)