Question

Evaluate (1^3+2^3+3^3)^1/2​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• $\sf (1^3 \: + \: 2^3 \: + \: 3^3)^{\scriptsize{\dfrac{1}{2}}}$

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• $\sf (1^3 \: + \: 2^3 \: + \: 3^3)^{\scriptsize{\dfrac{1}{2}}}$

Here,

• We can write $\sf {}^{\scriptsize{\dfrac{1}{2}}}$ as √.

Now,

• $\sf \sqrt{(1^3 \: + \: 2^3 \: + \: 3^3)}$

• $\sf \sqrt{1 \: + \: 8 \: + \: 27}$

• $\sf \sqrt{9 \: + \: 27}$

• $\sf \sqrt{36}$

• $\sf \sqrt{6^2}$

• 6

Therefore,

• $\sf (1^3 \: + \: 2^3 \: + \: 3^3)^{\scriptsize{\dfrac{1}{2}}} \: = \: 6$

Answer 2

$\large\bf\underline\red{Answer \: :-}$

Given :-

$\bigstar\sf{ \: (1 {}^{3} + 2 {}^{3} + 3 {}^{3} ) {}^{ \frac{1}{2} } }$

How to solve :-

We can write 1/2 to √

Required :-

$\longmapsto\sf{ \sqrt{(1 {}^{3} + 2 {}^{3} + 3 {}^{3} )} } \\ \\ \longmapsto\sf{ \sqrt{1 + 8 + 27} } \: \: \: \: \: \: \: \\ \\ \longmapsto\sf{ \sqrt{9 + 27} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \longmapsto\sf{ \sqrt{36} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \longmapsto\sf{ \sqrt{6 {}^{2} } } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \leadsto\sf\purple{ \boxed{ \sf{(1 {}^{3} + 2 {}^{3} + 3 {}^{3} ) {}^{ \frac{1}{2} } = 6 }}}$

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