Answer
351k+ 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.
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
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)