Question

4√2√3√729=p then the value of P20÷162+5/2?

1) 2
2) 1
3) 4
4) 3​

Answer 1

Answer:

Option 3

Step-by-step explanation:

Cube root of 729 is 9

Square root of 9 is 3

$\sqrt[4]{\sqrt[2]{\sqrt[3]{729} } } = p\\\\\sqrt[4]{\sqrt[2]{9} } = p\\\\\sqrt[4]{3} = p\\\\3 = p^{4}$

 

P ^ 20 can be written as P ^ 4 * P ^ 4 * P ^ 4 * P ^ 4 * P ^ 4  

P ^ 20 = 3 ^ 5 or 3 * 3 * 3 * 3 * 3 =  243

= 243 / 162 + 5 / 2

= 3 / 2 + 5 / 2

= 4 ans.

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } = p }$

Then the value of

$\displaystyle \sf{ \frac{ {p}^{20} }{162} + \frac{5}{2} = }$

1) 2

2) 1

3) 4

4) 3

EVALUATION

$\displaystyle \sf{ \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } = p }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{9 \times 9 \times 9} } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{ {9}^{3} } } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ 9 } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ {3}^{2} } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ 3 } }$

$\displaystyle \sf{ \implies {p}^{4} = 3 }$

Now

$\displaystyle \sf{ \frac{ {p}^{20} }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{{ ({p}^{4} )}^{5} }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{{ (3)}^{5} }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{81 \times 3 }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{ 3 }{2} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{ 3 + 5 }{2} }$

$\displaystyle \sf{ = \frac{ 8 }{2} }$

$\displaystyle \sf{ = 4 }$

FINAL ANSWER

Hence the correct option is 3) 4

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