Simplify- - 5- 813 - 2713-14

#160; [ 5[ 8^13 + 27^13]]^14 ⇒[5[(2^3)^13]+(3^3)^13]^14 ⇒[5[2+3]]^14 ⇒[5^2]^14 ⇒√(5) ...

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Byju's Answer

Standard VIII

Mathematics

Cube Root Using Prime Factorisation

Simplify: [...

Question

Simplify: ${⎡ ⎢ ⎣ 5 ⎡ ⎢ ⎣ 8^{\frac{1}{3}} + 27^{\frac{1}{3}} ⎤ ⎥ ⎦ ⎤ ⎥ ⎦}^{\frac{1}{4}}$

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Solution

${⎡ ⎢ ⎣ 5 ⎡ ⎢ ⎣ 8^{\frac{1}{3}} + 27^{\frac{1}{3}} ⎤ ⎥ ⎦ ⎤ ⎥ ⎦}^{\frac{1}{4}}$
$\Rightarrow [5 [(2^{3})^{\frac{1}{3}}] + (3^{3})^{\frac{1}{3}}]^{\frac{1}{4}} \Rightarrow [5 [2 + 3]]^{\frac{1}{4}} \Rightarrow [5^{2}]^{\frac{1}{4}} \Rightarrow \sqrt{5}$

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Similar questions

Q. Simplify the value of

(27^{\frac{1}{3}} \times 8^{\frac{1}{3}})

Q. Simplify :

{[5 {(8^{\frac{1}{3}} + 27^{\frac{1}{3}})}^{3}]}^{\frac{1}{4}}

Q. Write the value of

{\{5 (8^{1 / 3} + 27^{1 / 3})^{3}\}}^{1 / 4} .

Q. Simplify:

{(5 {(8^{1 / 3} + 27^{1 / 3})}^{3})}^{1 / 4}

Simplify
$\frac{(0.3)^{\frac{1}{3}} {(\frac{1}{27})}^{\frac{1}{4}} (9)^{\frac{1}{6}} (0.81)^{\frac{2}{3}}}{(0.9)^{\frac{2}{3}} (3)^{- \frac{1}{2}} {(\frac{1}{3})}^{- 2} (243)^{- \frac{1}{4}}}$

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Simplify: ⎡⎢⎣5⎡⎢⎣813+2713⎤⎥⎦⎤⎥⎦14

⎡⎢⎣5⎡⎢⎣813+2713⎤⎥⎦⎤⎥⎦14⇒[5[(23)13]+(33)13]14⇒[5[2+3]]14⇒[52]14⇒√5

Simplify: ${⎡ ⎢ ⎣ 5 ⎡ ⎢ ⎣ 8^{\frac{1}{3}} + 27^{\frac{1}{3}} ⎤ ⎥ ⎦ ⎤ ⎥ ⎦}^{\frac{1}{4}}$

${⎡ ⎢ ⎣ 5 ⎡ ⎢ ⎣ 8^{\frac{1}{3}} + 27^{\frac{1}{3}} ⎤ ⎥ ⎦ ⎤ ⎥ ⎦}^{\frac{1}{4}}$
$\Rightarrow [5 [(2^{3})^{\frac{1}{3}}] + (3^{3})^{\frac{1}{3}}]^{\frac{1}{4}} \Rightarrow [5 [2 + 3]]^{\frac{1}{4}} \Rightarrow [5^{2}]^{\frac{1}{4}} \Rightarrow \sqrt{5}$