Rewrite the expressions in the specified forms and find the required values.

1. [tex]8\sqrt{8}[/tex] can be written in the form [tex]8^k[/tex]. Find the value of [tex]k[/tex].

2. [tex]8\sqrt{8}[/tex] can also be expressed in the form [tex]m\sqrt{2}[/tex], where [tex]m[/tex] is a positive integer. Find the value of [tex]m[/tex].

3. Rationalize the denominator of [tex]\frac{1}{8\sqrt{8}}[/tex].

Give the answer in the form [tex]\frac{\sqrt{2}}{p}[/tex], where [tex]p[/tex] is a positive integer.

The value of k in the expression 8√8 is 3/2. The value of m when 8√8 is expressed in the form m√ 2 is 16. The denominator p of the rationalized fraction form √2/p is 8. ;

Answered by WilliamClarkGable | 2024-06-18

Not sure about first question
8√8 = 8(√4 x 2) (you can take the root of 4 out of the bracket) 8 x 2(√2) = 16√2
1/8√8 (to rationalise multiply by √8/√8 to eliminate the √8 from the denominator and so that it is only multiplied by 1 so has to be √8/√8) 1/8√8 x √8/√8 = 1√8/(8 x √8 x √8) = 1√8/(8 x 8) = 1√8/64
which can simplify
1√8/64 = 1(√4 x 2)/64 = 2√2/64

Answered by RhysH | 2024-06-24

In summary, the value of k for the expression 8 8 ​ is 3 4 ​ , and the value of m when expressed as m 2 ​ is 16 . After rationalizing the denominator of 8 8 ​ 1 ​ , we find that p = 32 .
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Answered by RhysH | 2024-09-03