Question

Please help me in question 13,14,16

Answer 1

${ \Huge{ \textbf{13)}}}$

${ \large{Area \: \: of \: \: rectangle =(16 \times 15) \: {m}^{2} }}$

And,

${ \red{ \tiny{Area \: \: of \: \: square = Area \: \: of \: \: rectangle}}}$

Therefore,

${ \huge{Area \: \: of \: \: square}} \\ \\ = > {(side)}^{2} = (16 \times 15) \: {m}^{2} \\ \\ = > side = \sqrt{16 \times 15} \\ \\ = > side = { \red{4 \sqrt{15} \: m \: \: or \: \: 15.49 \: m}}$

${ \blue {\Huge{14)}}}$

The five natural numbers being multiple of 3 are 3, 6, 9, 12, and 15.

Now,

${ \large{Cubes \: \: of \: \: the \: \: numbers \: \: above}} \\ \\ = > {(3)}^{3} = 27 \\ = > {(6)}^{3} = 216 \\ = > {(9)}^{3} = 729 \\ = > {(12)}^{3} = 1728\\ = > {(15)}^{3} = 3375$

Yes, It is positively verified that the cubes of first five natural numbers are the multiple of 27.

${ \green {\Huge{16)}}}$

${ \large{210125 = 5 \times 5 \times 5 \times 41 \times 41}}$

So, We need to multiply 210125 with 41 so as to get a cube number.

${ \large{The \: \: product \: \: so \: \: found \: \: will \: \:be = 210125 \times 41 = 8615125}}$

Now,

${ \huge { \red{\sqrt[3]{8615125} = 205}}}$