Answer :
Answer: " 3.344 " .
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Step-by-step explanation:
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Note: √5 = [tex]5^{(1/2)}[/tex] .
→ {Since: [tex]\sqrt{5} = \sqrt[2]{(5^1)} = \sqrt[2]{5}[/tex] } ;
and note the following property of "roots" :
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→ [tex]\sqrt[n]{x^y} = x^{(y/n)}[/tex] '
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[tex]\sqrt[4]{5} = 5^{(1/4)}[/tex] .
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→ [tex]\sqrt{5} * \sqrt[4]{5}[/tex] ;
= [tex]5^{(1/2)}[/tex] * 5^{(1/4) ;
= [tex]5^{[(1/2) +(1/4)]}[/tex] ;
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Note: Refer to the following property of exponents:
→ xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾
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Now, (1/2) + (1/4) = ? ;
Note: (1/2) = (?/4) ?? ;
→ Look at the "denominators" ;
2 * ? = 4 ? '
→ 4 ÷ 2 = ? ;
→ 4 ÷ 2 = 2 .
→ So: 2 * 2 = 4; ;
→ Now, look at the "numerators" ;
1 * 2 = 2 ;
So, (1/2) = (2/4) ;
→ (1/2) + (1/4) = (2/4) + (1/4) = (2 + 1) / 4 = 3/4 .
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So: [tex]5^{[(1/2) +(1/4)]}[/tex] ;
= [tex]5^{3/4)]}[/tex] ;
= 3.34370152488 ; (using calculator) ;
→ round to: " 3.344 ".
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