Answer

Verified

304.5k+ views

**Hint:**For solving this type of questions you should know about general mathematics calculations. In these problems, we will simply just find the values of the cubes of the given numbers and then add them and then we will take their square roots and solve them.

**Complete step by step answer:**

According to our question, we have to find the values of some of the given expressions. For solving these expressions, first we will find the values of the given terms as cube form. And then we will find the submission as asked in the question and then take the square root of that number. So, let us solve each of them one by one.

A. (i) ${{2}^{3}}+{{1}^{3}}$

As we know that,

$\begin{align}

& {{1}^{3}}=1\times 1\times 1=1 \\

& {{2}^{3}}=2\times 2\times 2=8 \\

\end{align}$

So, we will substitute these values in the expression and get,

$=1+8=9$

(ii) $\sqrt{{{1}^{3}}+{{2}^{3}}}$

As we know that,

$\begin{align}

& {{1}^{3}}=1\times 1\times 1=1 \\

& {{2}^{3}}=2\times 2\times 2=8 \\

\end{align}$

So, we will substitute these values in the expression and get,

$=\sqrt{1+8}=\sqrt{9}=3$

B. $\sqrt{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}$

As we know that,

$\begin{align}

& {{1}^{3}}=1\times 1\times 1=1 \\

& {{2}^{3}}=2\times 2\times 2=8 \\

& {{3}^{3}}=3\times 3\times 3=27 \\

\end{align}$

So, we will substitute these values in the given expression and so we get,

$=\sqrt{1+8+27}=\sqrt{1+35}=\sqrt{36}=6$

C. $\sqrt{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}}$

As we know that,

$\begin{align}

& {{1}^{3}}=1 \\

& {{2}^{3}}=8 \\

& {{3}^{3}}=27 \\

& {{4}^{3}}=4\times 4\times 4=64 \\

\end{align}$

So, we will substitute these values in the given expression and so we get,

$=\sqrt{1+8+27+64}=\sqrt{36+64}=\sqrt{100}=10$

D. $\sqrt{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}+{{5}^{3}}}$

As we know that,

$\begin{align}

& {{1}^{3}}=1 \\

& {{2}^{3}}=8 \\

& {{3}^{3}}=27 \\

& {{4}^{3}}=64 \\

& {{5}^{3}}=5\times 5\times 5=125 \\

\end{align}$

So, we will substitute these values in the given expression and so we get,

$=\sqrt{1+8+27+64+125}=\sqrt{100+125}=\sqrt{225}=15$

So, these are the values that we got.

**Note:**While solving such questions you have to be careful about the calculations because there are not many methods for solving them. But the only important thing is the calculations, so take the cubes accurately and then take the square root carefully, otherwise the whole solution will be wrong.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a stanza wise summary of money madness class 11 english CBSE

Which places in India experience sunrise first and class 9 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Which neighbouring country does not share a boundary class 9 social science CBSE

What is Whales collective noun class 10 english CBSE