Question

5√1024
$\sqrt[5]{1024}$
​

Answer 1

Required Solution :

$\longrightarrow \sf{ \sqrt[5]{1024}}$

As we know that,

• $\longrightarrow \sf{ \sqrt[n]{a} = a^{\frac{1}{n} }}$

$\longrightarrow \sf{ \sqrt[5]{1024} = 1024^{\frac{1}{5} } }$

Now, resolve the 1024 into prime factors, we get that :

$\longrightarrow \sf { 1024 =4 \times 4 \times 4 \times 4 \times 4 }$

$\longrightarrow \sf { 1024 =4^5 }$

Substitute the value $\longrightarrow \sf { 4^5 }$ at the place of 1024.

$\longrightarrow \sf{ \sqrt[5]{1024} = 4^{\not {5}(^{\frac{1}{\not5} })} }$

$\longrightarrow \underline{ \boxed{\sf{ \sqrt[5]{1024} = 4}}} \; \bigstar$

Therefore, $\sf{ \sqrt[5]{1024}}$ is 4.

More information :

Indices identities

$\boxed{ \begin{array}{cc} { \sf{ \star \: \: {( \sqrt{a} )}^{2} = a } } \\ \\ \star \: \: \sf \sqrt{a} \sqrt{b} = \sqrt{ab} \\ \\ \star \: \: \sf \dfrac{ \sqrt{a} }{ \sqrt{b} } = \sqrt{ \dfrac{a}{b} } \\ \\ \star \: \: \sf( \sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} ) = a - b \\ \\ \star \: \: \sf( \sqrt{a} \pm \sqrt{b} ) {}^{2} = {a}^{2} \pm2 \sqrt{ab} + b \\ \\ \star \: \: \sf{ (a + \sqrt{b})(a - \sqrt{b} ) = {a}^{2} - b } \end{array}}$

Laws of exponents :

$\boxed{\begin{array}{cc}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{array}}$